UNIVERSITY  OF  CALIFORNIA. 


Class 


THE  STEAM  ENGINE  INDICATOR 


Published    by  the 

McGrawrHill    Book.  Company 

^ 


Successors  to  theBookDepartments  of  tKe 

McGraw  Publishing  Company  Hill  Publishing"  Company 

Publishers   of  E>ook»s  for 

Electrical  World  TKe  Engineering  and  Mining  Journal 

TKe  Engineering  Record  Power  and  TKe  Engineer 

Electric  Railway  Journal  American   Machinist 


THE 

STEAM  ENGINE  INDICATOE 


BY 

F.  R.   LOW 

Editor  of  POWER  and  THE  ENGINEER 


THIRD  EDITION,    REVISED  AND    ENLARGED 


McGRAW-HILL   BOOK   COMPANY 

239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LONDON,  E.G. 

1910 


Copyright,  1910 

BY  THE 

McGRAW-HILL   BOOK   COMPANY 


PREFACE 


THE  steam-engine  indicator  has  become  at  once  the  tool  of  a  trade 
and  the  instrument  of  a  science.  The  operating  engineer  employs  it 
to  perfect  the  adjustment  of  valves  and  to  measure  power,  the  physicist 
to  investigate  thermodynamic  transfers  and  to  trace  the  cycle  of  the  heat 
engine.  It  is  to  steam  engineering  at  once  the  commercial  scale  and  the 
chemical  balance. 

The  following  contributions  to  the  literature  of  the  instrument  and 
its  diagrams  have  been  prepared  from  time  to  time  by  the  writer  for  the 
columns  of  Power,  and  are  addressed  to  the  practical  man  who  desires 
to  apply  the  indicator  as  an  instrument  of  ordinary  precision  to  the  prob- 
lems of  steam-engine  design  and  operation. 

F.   R.  LOW. 


211748 


CONTENTS 


CHAPTER  I 

SELECTION  AND  CARE  OF  THE  INSTRUMENT 

Degree  of  accuracy  required — Lightness — Freedom  from  friction — Paral- 
lelism— Lost  motion — Proportional  movement — The  spring — Size  of  drum — 
Vacuum  springs — Scales — Duplicate  parts — Leads — Lubrication — Paper. 


CHAPTER   II 

REDUCING  MOTION 11 

The  pendulum  lever — Directions  for  proportioning  and  for  leading  off  the 
cord — Defects  of  pendulum  motions — Lever  of  fixed  length — Lever  of  variable 
length — Connection  to  cross-head — Distortion  from  improper  connection — The 
pantograph — Adjusting  the  length  of  diagram — Setting  the  pantograph — Locat- 
ing the  pantograph — Reducing  wheels — Testing  the  accuracy  of  the  motion. 


CHAPTER   III 

APPLICATION 27 

Location  of  instrument — Tapping  the  cylinder — Cock  connections — Side 
pipes  and  three-way  cocks — Objectionable  connections — Attaching  the  instru- 
ment— The  cord — Management  of  the  cord — Centering  the  diagram — Drum 
tension — Preparing  and  fixing  the  lead — Selection  of  springs — Lubrication — 
Testing  in  position — Putting  on  the  card — Care  of  instrument  after  use. 


CHAPTER   IV 

THE  DIAGRAM 40 

Graphic  representation  applied  to  the  action  of  steam  in  the  cylinder — The 
ideal  diagram — Departures  therefrom  in  the  actual — Definition  of  the  various 
lines. 


viii  CONTENTS 


CHAPTER  V 

PAGE 

THE  ADMISSION  LINE 44 

Typical  admission  lines — The  proper  form — Effect  of  late  admission — Of 
tardy  exhaust  closure — Loops  due  to  lateness — Loops  due  to  excessive  com- 
pression— Points  at  top  of  admission  line — Effect  of  excessive  lead. 

CHAPTER   VI 

THE  STEAM  LINE 47 

The  loss  from  boiler  pressure — The  desirable  form — Effect  of  wire-drawing 
— Steam-chest  diagrams — Locating  cause  of  loss  of  pressure — Proportioning 
steam  mains  arid  ports — Initial  humps  in  steam  lines — Effects  of  increased  pis- 
ton speed — Throttle-governed  engines — Diagrams  without  any  steam  line- 
Modified  by  the  admission. 


CHAPTER   VII 

THE  EXPANSION  LINE 53 

Relation  of  volume  and  pressure  in  a  perfect  fluid — Rule  for  finding  the  pres- 
sure at  any  point  in  the  stroke — Plotting  the  expansion  curve  by  several  meth- 
ods— Determining  the  point  of  cut-off — Locating  the  clearance  line — What 
the  theoretical  expansion  line  shows — Departures  from  it  in  practice — 
Transparent  chart  of  theoretical  expansion  lines  and  its  use. 


CHAPTER   VIII 

THE  POINT  OF  RELEASE 64 

The  desirable  form — The  form  to  be  avoided — A  frequently  necessary  com- 
promise— Value  of  early  release  with  condenser— Effect  of  terminal  pressure 
— Loop  from  excessive  expansion. 

CHAPTER   IX 

THE  COUNTER-PRESSURE  LINE 67 

The  unbalanced  or  effective  pressure — Effect  of  pipe  and  port  friction — Pro- 
portioning exhaust  pipes  and  ports — Back  pressure  inappreciable  with  good 
design — Uniform  back  pressure — Effect  of  tardy  release  and  compression — 
Humps  in  compression  line — Effect  of  excessive  compression. 

CHAPTER   X 

THE  COMPRESSION  LINE 70 

The  inverse  of  expansion — Same  curve  applicable  to  the  ideal  case — Locat- 
ing clearance  line  from  compression  curve — Compression  in  a  condensing  engine 
— Effect  of  counter  pressure  on  compression — Use  of  compression  in  taking 


CONTEXTS  ix 

PAGE 

up  the  momentum  of  the  moving  parts — Effect  of  compression  on  clearance 
loss — Amount  of  compression  advisable— Typical  compression  lines — Loop 
from  excessive  compression — Falling  off  from  the  ideal  curve — Effects  of  con- 
densation and  leakage. 

CHAPTER  XI 

MEASUREMENT  OF  THE  DIAGRAM  FOR  MEAN  EFFECTIVE  PRESSURE 77 

The  "mean  effective  pressure  "  explained — The  ordinate  method — Spacing 
the  ordinates — Measuring  the  ordinates.— Use  of  parallel  rules  and  engineer's 
scales — Measuring  negative  loops. 

CHAPTER   XII 

THE  PLANIMETER 83 

The  mean  height  of  the  diagram  is  proportional  to  the  mean  effective  pres- 
sure— Reducing  the  diagram  to  its  mean  height  from  its  known  area — Use  of 
planimeter  for  determining  area — Description  of  instrument — Reading  the  ver- 
nier— Best  position  for  use — Tracing  the  diagram — Treatment  of  loops — Check- 
ing the  readings — Measuring  the  length  of  the  diagram — Rule  to  find  the  mean 
effective  pressure — Planimeters  with  adjustable  tracing  arms — Reading 
directly  in  horse-power — Directions  for  making  and  using  the  hatchet  planim- 
eter— The  Coffin  averaging  instrument. 


CHAPTER  XIII 

COMPUTING  THE  HORSE-POWER : 96 

Force — Work — The  foot  pound^-The  horse-power — Simple  formula  for 
horse-power — Rules  and  examples — The  horse-power  constant — Rule  for  find- 
ing same — Table  of  horse-power  constants — Use  of  table — Allowing  for  the 
piston  rod — The  power  of  the  individual  strokes — Balancing  the  effort. 


CHAPTER  XIV 

MEAN  EFFECTIVE  PRESSURE  AND  POINT  OF  CUT-OFF  BY  COMPUTATION 113 

Relation  of  hyperbola  to  containing  rectangle — Directions  for  finding  the 
mean  pressure  represented  by  an  ideal  diagram  of  a  given  pressure  and  ratio 
of  expansion — Allowing  for  departures  from  the  ideal — Table  for  computing 
mean  and  initial  pressures,  points  of  cut-off,  ratios  of  expansion  and  clearance 
— Examples — The  effect  of  clearance — The  real  and  apparent  ratios  of  expan- 
sion. 

CHAPTER   XV 

STEAM  CONSUMPTION  FROM  THE  DIAGRAM 119 

Volume  generated  per  hour  per  horse-power — Value  of  ihat  volume  in 
pounds  of  steam — Correction  of  volume  for  clearance — Rule  to  find  steam  con- 


CONTENTS 


13750 

sumption  from  diagram — Example — Table  of  values  of  — Volume  of  new 

JVl.xLi.-r. 

steam  indicated  by  distance  between  expansion  and  compression  lines — Rule 
for  determining  consumption  by  this  line — Computing  steam  consumption 
from  compound  engine  diagrams. 


CHAPTER   XVI 

DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  NEGLECTED 134 

Use  of  different  scales  for  the  different  cylinders — Reducing  diagrams  to  the 
same  scale — Comparison  of  diagrams  in  this  condition — Reduction  of  diagram 
to  same  scales  of  volumes — The  combined  diagrams — Comparison  of  the  com- 
bined diagram  with  the  ideal. 


CHAPTER   XVII 

DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  CONSIDERED 139 

Locations  of  the  diagrams  with  reference  to  the  line  of  zero  volume — Rela- 
tion of  the  steam  line  of  the  low-pressure  diagram  to  the  counter-pressure  line 
of  the  high — Effect  of  receiver  capacity — Effect  of  change  of  load — Effect  of 
varying  cut-off  in  low-pressure  cylinder. 


CHAPTER  XVIII 

ERRORS  IN  THE  DIAGRAM 145 

Error  from  the  use  of  the  pendulum  motion — Error  with  lever  of  fixed  length 
vibrating  90° — Error  with  same  lever  vibrating  35°  to  40° — Amount  of  error 
allowable — Error  from  lack  of  parallelism  between  cord  and  guides — Error  due 
to  indirect  connection  of  indicator. 

CHAPTER   XIX 

MEASURING  THE  CLEARANCE 155 

Direction  for  measuring  by  equal  volumes  of  water — Correction  for  riser  pipe 
— By  calculated  volume  of  water — By  weight  of  water — By  time  required  to 
fill — Professor  Sweet's  method  of  equal  weights — Diagram  to  determine 
without  calculation  the  proportion  of  clearance  to  displacement. 


THE   STEAM  ENGINE   INDICATOR 

CHAPTER  I 
SELECTION  AND  CARE   OF  THE   INSTRUMENT 

THERE  are  at  this  writing  nine  or  ten  different  steam  engine  indicators 
upon  the  market.  As  a  guide  to  its  readers  in  determining  which  of 
these  is  best  suited  to  their  purpose,  it  shall  be  the  province  of  this  work 
only  to  specify  the  requirements  of  a  perfect  instrument,  point  out 
the  possible  sources  of  error  in  the  instrument  as  made,  detail  the 
methods  of  testing  foi  such  faults,  and  leave  the  reader  to  purchase 
the  degree  of  accuracy  necessary  for  his  purpose  at  the  lowest  available 
price. 

For  certain  classes  of  work,  such  as  the  ordinary  setting  of  valves, 
the  measurement  of  horse-power  for  purposes  of  daily  record  in  factory 
work,  etc.,  extreme  accuracy  is  not  essential.  A  man  does  not  buy 
a  chemist's  balance  to  weigh  sugar,  nor  an  expensive  chronometer  for 
a  kitchen  clock.  An  instrument  which  is  ordinarily  correct  will  answer 
many  purposes  to  which  an  indicator  may  be  advantageously  applied, 
and  its  inherent  errors  will  probably  be  less  than  those  of  manipula- 
tion and  observation. 

For  other  classes  of  work,  however,  the  utmost  attainable  precision 
must  be  insisted  upon,  and  the  very  best  instruments  made  are  not 
good  enough.  In  a  72-inch  low-pressure  cylinder  there  will  be  developed 
over  100  horse-power  per  pound  of  mean  effective  pressure.  The  varia- 
tion of  one  one-hundredth  of  an  inch  in  the  mean  height  of  a  diagram 
from  one  end  of  this  cylinder  would  mean,  with  a  10-pound  spring,  a 
difference  of  over  five  horse-power  in  the  result.  If  this  engine  were  in  a 
vessel,  built  as  others  have  been  with  a  bonus  or  forfeit  of  one  hundred 
dollars  per  horse-power  above  or  below  that  called  for  in  the  contract,  the 
omney  involved  in  its  exact  determination  would  warrant  the  extreme 
of  expense  and  pains  in  securing  the  utmost  attainable  precision  in  the 
measuring  instruments. 


THE   STEAM   ENGINE   INDICATOR 


In  a  perfect  indicator  the  pencil  should,  by  its  vertical  position  on 
the  diagram,  represent  exactly  the  pressure  beneath  the  indicator  pis- 
ton at  any  instant;  and  by  its  horizontal  position,  the  point  which  the 
piston  has  reached  in  its  stroke  at  the  same  instant.  This  simple  con- 
dition is  impossible  of  attainment  in  practice,  from  the  fact  that  the 
materials  of  which  indicators  are  made  have  mass.  As  soon  as  they 
are  put  into  motion  we  have  momentum  to  carry  both  the  pencil  and 
the  drum  away  from  the  point  to  which  they  would  have  been  carried 
by  the  pressure  and  reducing  -motion  alone,  and  their  inertia  to  prevent 
their  instantaneous  response  to  a  change  in  conditions. 

Lightness. — It  may,  therefore,  be  concluded  that,  other  things  being 
equal,  that  instrument  will  give  the  best  results  in  which  the  least  weight 
is  moved  through  the  least  distance  for  the  production  of  diagrams  of 
equal  size,  assuming  always  that  enough  material  is  used  to  give  the 
necessary  strength  and  rigidity. 

Freedom  from  Friction  is  a  quality  that  an  indicator  should  possess 
in  the  greatest  possible  degree.  Detach  the  piston  and  see  that  the  pencil 

levers  will  drop  freely  and  with- 
out any  suspicion  of  a  catch  from 
any  position  within  the  working- 
range  of  the  instrument.  With 
the  piston  attached,  but  without  any 
spring,  raise  the  piston  by  taking 
hold  of  the  pencil  delicately,  and 
work  the  pencil  lever  up  and 
down  through  the  full  limit  of  its 
motion,  feeling  carefully  for  any 
interruption  to  its  movement. 
Then  raising  the  pencil  nearly  to 
the  top  of  the  paper-drum,  cover 
the  hole  through  which  steam  is 
admitted  to  the  indicator  with  the 
thumb,  as  in  Fig.  1.  The  pencil 
FIG.  1.  should  sink  slowly  through  the 

whole    range    of    its    motion,    but 

should    drop    instantly    from    any    point    upon    the    removal    of    the 
thumb. 

Do  not  get  the  piston  too  tight  through  fear  of  its  leaking.  It 
has  a  whole  boilerful  of  steam  behind  it  part  of  the  time,  and  a 
large  volume  always,  and  no  noticeable  difference  in  pressure  will 
result  from  any  leakage  which  can  take  place  unless  the  leakage  is  so 
excessive  as  to  increase  the  pressure  on  top  of  the  piston.  On  condens- 
ing engines  the  vacuum,  as  indicated  by  the  indicator,  may  be  materially 


SELECTION  AND  CARE   OF  THE  INSTRUMENT  3 

reduced  if  the  piston  is  too  loose,  and  it  is  unpleasant  and  uncleanly  to 
have  too  much  steam  and .  water  leaking  and  spattering  about  the 
instrument.  The  piston  which  will  sustain  the  test  shown  in  Fig.  1 
will  be  found  tight  enough  without  excessive  friction. 

Parallelism. — The  line  in  which  the  point  of  the  pencil  moves  should 
be  parallel  with  the  axis  of  the  paper-drum,  in  order  both  that  the  pencil 
may  bear  upon  the  paper  equally  in  all  portions  of  its  stroke,  and  that 
its  vertical  movement  may  be  at  right  angles  with  the  horizontal  move- 
ment of  the  paper.  With  the  piston  attached  but  with  no  spring,  adjust 
the  stop  so  that  you  can  just  see  daylight  between  the  point  of  the  pencil 
and  the  paper  on  the  drum.  Then  raise  the  pencil  slowly 
through  its  full  range  by  pushing  the  piston,  and  notice  if  the 
pencil  point  keeps  the  same  distance  from  the  paper.  If  it  does 
not,  either  the  spindle  of  the  barrel  is  out  of  line  with  the 
indicator  cylinder,  or  the  pencil  motion  is  out  of  line.  Still 
sighting  between  the  pencil  and  the  paper,  rotate  the  barrel  by 
drawing  out  the  cord.  If  the  paper  touches  the  pencil, 
or  moves  away  from  it,  the  drum  is  out  of  shape  or 
improperly  centered.  Now,  allowing  the  pencil  to 
touch  the  paper,  push  the  piston  upward,  drawing  a 
fine  vertical  line  upon  the  card;  then,  with  the  spring 
attached,  rotate  the  barrel,  and 
draw  a  fine  horizontal  line.  These 
lines  should  be  perfectly  straight 
throughout  their  lengths,  and  at 
right  angles  with  each  other,  a 
condition  which  may  be  tested 
with  the  triangles  after  the  card 
is  removed  from  the  paper-drum  as 
FIG.  2.  shown  in  Fig.  2. 

If  the  lines  do  not  comply  with 

these  conditions,  the  natural  inference  will  be  that  the  pencil  movement 
is  incorrect,  although  the  horizontal  line  may  be  thrown  out  by  any 
vertical  movement  of  the  cylinder  upon  its  spindle. 

Lost  Motion  is  usually  a  matter  more  of  adjustment  than  of  manu- 
facture. Put  a  stiff  spring  into  the  indicator,  and  carefully  feel  at  the 
end  of  the  pencil  lever  for  any  unrestrained  movement.  Should  such  be 
found,  its  cause  should  be  searched  for  in  the  connection  of  the  piston 
rod  to  the  piston  and  pencil  motion,  through  all  the  joints  of  the  parallel 
motion,  in  the  fit  of  the  collar  which  carries  the  mechanism,  and  if  it  can- 
not be  corrected  by  adjustment  without  making  the  instrument  too  stiff 
to  comply  with  the  friction  test  above  described,  the  instrument  should 
be  rejected. 


4  THE   STEAM   ENGINE   INDICATOR 

Proportional  Movement. — The  movement  of  the  pencil  should  be 
proportional  to  that  of  the  piston.  This  is  an  important  requirement, 
but  more  difficult  of  test.  A  screw  of  perfectly  uniform  pitch  should  be 
arranged  to  communicate  its  movement  to  the  indicator  piston.  With 
a  little  ingenuity  a  micrometer  caliper  can  be  adapted  to  this  purpose. 
Turn  the  screw  up  until  it  has  a  firm  bearing  against  the  piston,  then 
apply  the  pencil  of  the  indicator  to  the  paper  and  make  a  line  by  moving 
the  drum.  Then  turn  the  screw  through  a  number  of  equal  distances, 
repeating  the  marking  process  each  time.  The  piston  having  been 
moved  through  an  equal  space  after  each  marking,  the  spaces  between 
the  lines  upon  the  paper  should  be  equal.  Care  must  be  taken  in  arrang- 


FIG.  3. 


FIG.  4. 


ing  and  manipulating  this  test.  The  pencil  movement  is  from  four  to 
six  times  that  of  the  piston,  and  any  failure  to  move  the  piston  through 
equal  spaces  will  introduce  apparent  errors  which  will  be  magnified 
upon  the  card. 

Count  the  spaces  between  the  lines  which  you  have  drawn,  then 
count  off  the  same  number  of  spaces  upon  an  equally  divided  scale  of 
such  magnitude  that  the  aggregate  length  of  the  given  number  of  spaces 
on  the  scale  will  not  be  less  than  the  distance  between  the  outside  lines 
upon  the  paper.  Then  lay  the  scale  across  the  pencil  lines,  as  shown  by 
Fig.  3,  in  such  a  way  that  the  number  of  spaces  laid  oft7  on  the  scale  will 


SELECTION   AND   CARP:   OF  THE   INSTRUMENT  5 

just  reach  from  the  top  to  the  bottom  line  on  the  diagram.  For  example, 
in  the  diagram  shown  in  Fig.  3  there  are  25  spaces.  A  "ten  to  the  inch" 
scale  is  laid  diagonally  across  with  its  zero  and  25  lines  upon  the  out- 
side lines  of  the  diagram.  If  the  lines  of  the  diagram  are  equally  spaced 
they  will  coincide  with  the  divisions  of  the  scale,  as  in  Fig.  3.  If  the 
multiplying  motion  of  the  indicator  is  incorrect  the  spaces  of  the  diagram 
will  be  unequal,  and  their  inequality  will  be  apparent  by  their  failure 
to  meet  the  divisions  of  the  scale,  as  in  Fig.  4. 

The  Spring  is  the  actual  measuring  factor  of  the  indicator,  and 
the  apparatus  required  for  its  testing  is  too  complicated  and  expensive 
to  be  at  the  command  of  the  average  purchaser.  The  test  ought  to  be 
made  under  as  nearly  as  possible  the  conditions  of  use, — i.e.,  under  steam 
pressure,  so  that  all  the  factors  of  temperature,  etc.,  will  be  present. 
Most  of  the  manufacturers  will  make  such  tests  of  springs  for  purchasers, 
and  the  diagrams  of  the  test  may  be  kept  as  a  record  of  the  degree  of 
accuracy  of  the  instrument  at  that  time.  It  is  well  also  to  have  such 
tests  made  occasionally  after  the  instrument  has  been  in  use,  and  espe- 
cially just  before  and  after  applying  it  to  work  of  particular  importance. 
The  test  consists  of  applying  steam  to  the  indicator  piston  at  pressures 
increasing  by  equal  amounts,  say,  for  ordinary  springs,  five  pounds. 
As  each  five  pounds  is  reached  a  line  is  drawn  upon  the  card,  a  standard 
gage  or,  better,  a  mercury  column,  being  used  to  indicate  the  pressures. 
The  pressure  is  then  allowed  to  fall,  and  marks  are  again  made  as  the  gage 
passes  the  points  which  were  noted  in  the  upward  series.  If  the  spring 
and  all  the  transmitting  and  recording  mechanism  were  perfect,  and  the 
indicator  without  friction,  the  spaces  for  equal  changes  in  pressure 
would  be  of  equal  width,  and  the  lines  indicating  the  same  pressures 
would  be  coincident,  whether  drawn  when  the  piston  was  going  up  or 
coming  down.  This  degree  of  perfection  is  rarely  if  ever  reached,  for 
even  if  the  spring  compresses  equal  distances  for  equal  increments  of 
pressure  throughout  its  entire  range,  and  its  movement  is  transmitted 
correctly  to  the  pencil,  the  friction  of  the  piston,  of  the  pencil  movement, 
and  of  the  pencil  on  the  paper  all  combine  in  opposing  the  motion  of  the 
piston  in  both  directions,  so  that  the  lines  of  the  upward  series  are  too 
low  and  those  of  the  downward  series  too  high  by  an  amount  .equivalent 
to  the  frictional  resistance  upon  the  scale  of  the  spring. 

A  very  small  amount  of  pressure  at  the  piston  would,  however,  take 
care  of  all  this,  so  that  the  wide  discrepancy  often  shown  between  the 
upward  and  downward  diagrams  is  more  liable  to  be  due  to  the  failure 
of  the  operator  to  catch  the  pencil  at  the  same  point  than  to  the  inordinate 
amount  of  friction  which  they  indicate. 

The  above  qualities  are  necessary  to  an  indicator  for  accuracy.  Other 
points,  more  in  the  nature  of  conveniences  than  essentials,  but  which 


6  THE   STEAM   ENGINE   INDICATOR 

may  be  well  considered  in  selecting  an  instrument,  are  the  comparative 
simplicity  of  changing  springs,  adjustment  for  height  of-  atmospheric 
line,  changing  from  right  to  left  hand  and  vice  versa,  adjusting  the  drum- 
spring  and  leading  pulley,  attaching  the  indicator  to  the  cock,  etc. 

Pencil  Holder. — For  holding  the  lead,  the  end  of  the  pencil  lever  in 
some  indicators  is  formed  into  a  light  steel  quill  of  a  size  which  will  hold 
the  lead  firmly  when  forced  through  it.  In  other  makes  the  end  of  the 
pencil  lever  is  reinforced  and  threaded  internally,  the  lead  being  screwed 
through  it.  The  preference  of  the  writer  is  decidedly  for  the  first  method. 
The  quill  being  split  lengthwise  adapts  itself  by  its  elasticity 'to  varying 
sizes  of  lead,  and  may  be  closed  with  a  pair  of  pincers  if  it  fails  to  close 
upon  a  lead  of  small  diameter  after  being  used  with  a  larger  size.  As 
the  point  is  shortened  by  resharpening,  the  lead  can  be  pushed  forward, 
and  if  it  breaks  off  short  it  is  easily  pushed  out  of  the  holder  with  a  match 
or  toothpick.  The  threaded  end  is  adapted  to  only  one  size  of  lead, 
which,  with  the  short  bearing  afforded,  is  apt  to  get  loose  and  wabble. 
If  it  breaks  off  short,  it  must  be  dug  out  of  the  threaded  portion;  and  if 
the  threaded  method  offers  any  compensating  advantages  the  author 
has  yet  to  learn  of  them. 

Selection  of  Springs.— If  the  use  of  the  instrument  is  to  be  confined 
to  one's  own  plant  it  is  easy  to  select  a  spring  or  set  of  springs  adapted 
to  the  pressures  and  speeds  to  be  encountered.  If  the  instrument  is 
to  be  used  promiscuously,  the  more  springs  the  operator  can  own  the 
better  will  he  be  equipped  to  meet  the  conditions  of  practice.  In  select- 
ing a  spring,  aim  to  get  as  large  a  diagram  as  possible  without  undue 
distortion.  If  a  diagram  be  taken  with  a  20  spring  an  error  of  measure- 
ment of  one  one-hundredth  of  an  inch  would  influence  the  results  only 
one-fifth  of  a  pound.  With  a  50  spring  the  same  error  in  measurement 
would  represent  a  departure  of  one-half  pound.  Or  since  the  average 
useful  pressure  upon  which  the  power  indicated  by  the  diagram  depends 
is  proportional  to  the  area  of  the  diagram,  consider  a  diagram  taken 
with  a  20  spring  having  an  average  height  of  2  inches  and  a  length  of 
4  inches  as  compared  with  one  taken  from  the  same  cylinder  with  a  40 
spring  and  a  length  of  2  inches.  The  area  of  the  first  diagram  would 
be  8  inches,  of  the  second  2  inches,  and  the  average  useful  or  "mean 
effective  pressure  "  of  course  40  in  both  cases. 

area        scale  area         scale 

8  X4  2°    =40.  2   X2  4°   =40. 

length  length 

In  the  large  diagram  40  pounds  of  pressure  are  represented  by  8  inches 
of  area,  or  5  pounds  to  an  inch,  and  an  error  in  measurement  of  the  area 


SELECTION   AND   CARE   OF  THE   INSTRUMENT  7 

of  one  one-hundredth  of  a  square  inch  would  involve  an  error  of  but 
five  one-hundredths  of  a  pound  in  the  indicated  pressure.  In  the  case 
of  the  smaller  diagram  40  pounds  pressure  is  represented  by  2  square 
inches  of  area,  20  pounds  to  the  inch,  and  a  deviation  of  one  one-hun- 
dredth of  a  square  inch  from  the  truth  in  measuring  this  area  will  involve 
an  error  of  two-tenths  of  a  pound. 

It  is  therefore  advisable  to  have  the  area  as  large  as  possible  and 
have  it  right. 

On  the  other  hand,  the  allowable  movement  of  both  the  pencil  and 
the  drum  is  limited  by  the  effects  of  momentum.  At  high  speeds  a 
light  spring  and  long  movement  of  the  drum  would  result  in  a  diagram 
so  distorted  by  the  effects  of  momentum  and  inertia  as  to  introduce 
errors  much  more  serious  than  those  which  are  likely  to  occur  from 
inaccurate  measurement  of  a  smaller  and  more  perfect  diagram.  The 
speed  as  well  as  the  pressure  will  therefore  have  a  bearing  upon  the 
spring  selected,  and  wrill  also  influence  the  selection  as  between  the 
standard  size  of  paper-drum  which  is  used  for  moderate  speeds,  and 
the  smaller  drums  which  some  of  the  makers  supply  for  high-speed  work. 
Some  manufacturers  furnish  two  sizes  of  drums,  which  may  be  used  inter- 
changeably upon  the  same  instrument,  adapting  it  to  higher  and  lower 
speeds. 

In  some  instruments  the  position  of  the  atmospheric  line  is  fixed, 
in  others  it  is  adjustable,  so  that  in  indicating  a  non-condensing  engine 
the  base  line  may  be  lowered  and  the  whole  of  the  allowable  movement 
of  the  pencil  utilized  for  the  height  of  the  diagram.  The  springs  made 
by  American  manufacturers  are  usually  scaled  decimally,  that  is,  10, 
20,  30,  40,  etc.,  pounds  to  the  inch. 

Vacuum  Springs. — It  is  frequently  desirable  in  condensing  engines  to 
obtain  the  lower  or  condensing  portion  of  the  diagram  upon  a  larger 
scale  than  that  of  the  spring  available  with  the  initial  pressure  used. 
With  an  initial  pressure  which  demands  a  60  spring,  a  realized  vacuum 
of  12  pounds  would  be  represented  by  a  line  only  one-fifth  of  an  inch 
below  the  atmospheric  line,  Fig.  5,  giving  a  very  small  area  to  th3 
condenser  portion  of  the  diagram.  In  order  to  obtain  this  area  upon 
a  larger  scale,  giving  increased  accuracy  of  measurement,  showing  more 
clearly  the  points  of  release  and  compression,  etc.,  springs  of  low  tension 
are  sometimes  fitted  with  bosses  or  studs,  which  prevent  their  closing 
beyond  a  certain  point,  while  they  are  free  to  extend  to  any  amount. 

In  Figs.  '5  and  6  are  shown  two  diagrams,  the  first  drawn  to  a  60 
scale;  and  in  Fig.  6  the  shaded  portion  of  the  first  diagram  is  shown 
expanded  to  a  10  scale.  Notice  how  much  more  prominently  the  points 
of  release  and  compression  are  shown,  on  account  of  the  more  rapid 
vertical  movement  with  the  same  horizontal  movement;  and  how  much 


8 


THE   STEAM   ENGINE   INDICATOR 


less  an  error  of  a  few  hundredths  of  a  square  inch  in  measuring  the  area 
of  the  condensing  portion  of  the  card  would  affect  the  result.  A  spring 
made  especially  for  this  purpose  by  the  American  Steam  Gauge  Co. 


is  shown  in  Fig.  7.  It  is  wound  so  closely  that  the  coils  close  upon 
themselves  before  the  pencil  movement  can  attain  a  dangerous  amount 
of  motion.  The  large  number  of  coils  lying  in  so  nearly  a  horizontal 


Atmospheric  Line 


FIG.  6. 


direction  admits  of  sufficient  elasticity  with  a  good-sized  wire,  while 
there  is  a  uniformity  of  movement  throughout  the  desired  range.  These 
springs  are  scaled  for  extension  only. 


SELECTION   AND   CARE   OF  THE   INSTRUMENT  9 

Scales. — For  a  measuring  scale,  the  author  uses  a  6-inch  engineer's 
rule,  triangular  in  cross-section,  as  shown  in  Fig.  8,  and  graduated  upon 
its  six  edges  to  20ths,  30ths,  40ths,  50ths,  GOths,  and  SOths  of  an  inch. 
This  rule  not  only  furnishes  the  six  scales  mentioned  in  one  rule,  but 
by  estimating  half  spaces  a  50  scale  can  be  used  for  100  and  the  60  for 
120,  etc.  With  the  lower  scales,  where  the  distances  are  greater,  half 
pounds  can  be  measured  accurately  by  using  the  60  scale  for  a  30  spring 
or  the  40  for  a  20,  the  20  for  a  10,  etc.  The  50  scale  is  also  useful  for 
measuring  the  length  of  the  diagram,  each  division  representing  0.02 
of  an  inch,  and  the  length  of  6  inches  being  more  than  sufficient  for 
any  diagram. 

Duplicate  Parts. — Much  annoyance  and  loss  of  time  may  be  saved 
by  carrying  in  the  indicator  box  duplicates  of  those  parts  liable  to  loss 


40 

FIG.  7.  FIG.  8. 

or  derangement.  An  additional  drum-spring,  and  two  or  three  of  the 
smaller  screws  which  have  to  be  frequently  removed  in  changing  springs, 
etc.,  and  which  are  liable  to  disappear  down  a  crack  or  somewhere  else 
when  most  wanted,  will  allow  a  test  to  proceed  smoothly,  when  its 
interruption  would  be  particularly  annoying  from  the  insignificance  of 
its  cause. 

Leads. — Select  a  hard  lead  of  good  smooth  quality  and  of  small 
diameter,  and  use  but  a  small  piece  at  a  time.  At  the  end  of  the  pencil 
lever,  where  the  motion  is  greatest,  the  weight  should  be  reduced  to 
the  smallest  possible  value.  If  pointed  with  a  fine  file,  and  rubbed  down 
with  an  emery  stick,  such  as  is  used  for  sharpening  draftsmen's  pencils, 
or  a  fine  stone,  it  will  wear  longer  and  be  smoother  and  more  satisfac- 
tory than  if  whittled  into  shape.  A  little  metallic  case  of  such  leads 
already  pointed  is  a^very  convenient  portion  of  an  outfit. 


10  THE   STEAM  ENGINE   INDICATOR 

Lubrication. — For  lubricating  the  bearings  of  the  instrument  a  light 
machinery  oil,  one  which  will  not  gum  or  corrode,  should  be  used.  A 
small  vial  of  such  oil  usually  accompanies  the  instrument,  some  makers 
furnishing  porpoise  oil,  such  as  is  used  for  clocks  and  watches.  The 
piston,  however,  is  better  lubricated  with  cylinder  oil,  and  the  small 
flat  cans  which  are  furnished  for  bicyclists'  use,  and  which  fit  readily 
into  the  tray  of  the  indicator  box,  furnish  a  convenient  means  of  carry- 
ing a  filtered  supply  in  a  form  readily  available  for  cleanly  use.  The 
manufacturer's  filtering  should  not  be  accepted.  Filter  the  oil  carefully 
yourself,  and  see  that  the  can  is  perfectly  clean.  A  small  particle  of 
grit  upon  the  piston  of  an  indicator  will  not  only  throw  the  diagram 
into  the  most  unaccountable  contortions,  but  may  scratch  and  injure 
both  cylinder  and  piston  to  a  serious  degree. 

Paper. — Use  hard,  tough,  smoothly  calendered  paper  of  a  width 
sufficient  to  include  the  highest  allowable  pencil  travel  and  about  an 
inch  longer  than  the  circumference  of  the  barrel.  Such  paper  can  be 
procured  cut  to  the  desired  size,  of  almost  any  printer.  If  a  blank 
form  is  printed  upon  the  back  for  the  recording  of  data  and  observations, 
do  not  allow  the  printer  to  use  so  much  impression  as  to  spoil  the 
smoothness  and  uniformity  of  the  surface  upon  which  the  pencil  works. 
I  have  seen  cards  so  roughened  up  by  leading  points  sticking  through 
that  it  would  be  a  wonder  if  a  diagram  could  be  drawn  without  the 
pencil  point  hitting  some  of  them. 

Metallic  paper  is  made  by  treating  ordinary  paper  with  sulphate  of 
zinc.  A  metallic  point  will  then  trace  a  line  upon  it  and  such  a  hard, 
sharp  point  may  be  used  instead  of  the  ordinary  lead. 

It  would  seem  as  though  a  tubular  or  trough  pen  might  be  made 
light  and  fine  enough  to  replace  the  pencil  point.  The  liquid  contact 
once  established,  scarcely  any  pressure  wrould  be  required  to  make  a 
record,  and  the  diagram  would  be  clean  cut  and  legible.  With  the  fine 
point  and  light  pressure  necessary  with  a  pencil  the  diagram  is  often 
hard  to  see,  and  is  quickly  obliterated  by  handling.  If  inked  in  by 
hand  there  is  always  a  question  of  the  accuracy  of  the  work  and  a  diagram 
originally  drawn  with  ink  would  present  so  many  advantages  that  it  is 
surprising  that  none  of  the  various  makers  has  applied  to  the  indicator 
this  device,  which  is  used  so  universally  upon  other  recording  apparatus. 


CHAPTER   II 
REDUCING  MOTION 

IN  order  to  use  the  indicator,  a  means  must  be  provided  for  mov- 
ing the  paper-drum  in  time  with  the  engine  piston.  This  movement 
is  usually  derived  from  the  cross-head,  and  the  appliance  used  to  reduce 
the  movement  to  that  adapted  to  the  paper-barrel  is  spoken  of  as  the 
"reducing  motion." 

The  Pendulum  Lever. — The  most  primitive  expedient  for  this  pur- 
pose is  a  lever  suspended  from  the  ceiling  or  other  suitable  support,  and 


connected  at  its  lower  end  with  the  cross-head  in  such  a  way  that  it 
will  be  swung  back  and  forth  as  the  engine  makes  its  revolutions,  as 
in  Fig.  9.  The  motion  of  the  lever  increases  from  nothing  at  the  point 
of  suspension  to  approximately  the  full  stroke  of  the  engine  at  the  cross- 

11 


12  THE   STEAM   ENGINE    INDICATOR 

head  end,  the  amount  of  motion  being  directly  proportional  to  the  dis- 
tance from  the  point  of  suspension.  A  point  midway  of  the  lever  would 
have  a  motion  equal  to  one-half  the  stroke;  one-quarter  of  the  way 
from  the  point  of  suspension,  one-quarter  stroke,  etc.  Letting 

/  =  distance  between  pivot  and  cord  pin, 

L=  length  of  lever, 

s=  desired  length  of  diagram, 

S  =  stroke  of  engine, 

then  the  diagram  will  be  yths  of  the  stroke,   and  the    cord  must   be 

attached  at  a  point  -^ths  of  the  total  length  of  the  lever  from  the  point 

o 

of  suspension.     For 

that  is,  as  the  distance  between  the  pivot  and  the  point  to  which  the 
cord  is  attached  is  to  the  total  length  of  the  lever,  so  is  the  motion  at 
that  point  and  the  length  of  the  diagram  to  be  derived  from  that  motion, 
to  the  stroke  of  the  engine. 

Is  Ls  IS 

-j  =-~     and     l=-^r     and     S=T~- 

To  Find  the  Point  of  Attachment,  or  the  distance  from  the  point 
of  suspension  at  which  the  cord  should  be  attached  to  produce  a 
given  length  of  diagram: 

RULE. — Multiply  the  total  length  of  the  lever  by  the  desired  length  of 
diagram,  and  divide  by  the  stroke  of  the  engine,  all  in  inches. 

EXAMPLE. — With  a  lever  60  inches  in  length  on  an  engine  of  24-inch 
stroke,  how  far  would  you  attach  the  cord  from  the  point  of  suspension 
to  produce  a  diagram  4  inches  in  length? 

60X4 
Operation :  =  10  inches. 

To  Find  the  Length  of  Diagram  produced  by  a  cord  at  a  given 
point  of  attachment: 

RULE. — Multiply  the  distance  from  the  pivot  to  the  point  of  attachment 
by  the  stroke  of  the  engine,  and  divide  by  the  total  length  of  the  lever,  all  in 
inches. 

EXAMPLE. — What  length  of  diagram  would  be  produced  by  attach- 
ing the  cord  4^  inches  from  the  pivot  on  a  lever  20  inches  in  length  at- 
tached to  a  cross-head  having  a  stroke  of  12  inches? 

4.5X12 

Operation:      "  =2.7  inches. 


REDUCING   MOTION 


13 


The  total  length  of  the  lever  is  measured  from  the  point  of  suspension 
to  the  point  of  attachment  to  the  cross-head,  and  is  variable  in  some 
of  the  arrangements  to  be  shown.  As  the  variation  bears  a  small  pro- 


FIG.  10. 


FIG.  11. 


portion  to  the  total  length,  and  the  length  of  diagram  is  usually  figured 
only  to  keep  within  the  limits  of  the  paper-drum,  especial  refinement 
in  this  particular  is  unnecessary.  In  order  to  get  the  full  motion  of 


FIG.  12. 


the  pin,  the  cord  must  be  led  off  in  the  direction  of  the  pin's  greatest 
movement,  i.e.,  at  right  angles  to  the  lever  when  the  lever  is  itself  at 
right  angles  to  the  guides.  It  will  be  readily  seen  that  if  the  cord  were 


14 


THE   STEAM   ENGINE   INDICATOR 


led  off  parallel  to  the  lever  it  would  receive  very  little  motion.  It  is 
desirable  to  avoid  the  use  of  leading  pulleys  as  in  Fig.  9;  and  Figs.  10 
and  11  show  two  methods  of  accomplishing  this,  the  latter  by  putting 
on  a  segment  of  a  circle,  called  a  brumbo  pulley,  having  a  radius  equal 
to  the  distance  /  from  the  pivot  to  the  point  of  attachment  of  the  cord, 
and  so  placed  that  the  cord  may  be  led  straight  to  the  indicator  without 
running  on  to  the  corners  of  the  segment  at  the  extremes  of  the  stroke. 
In  Fig.  10  a  supplementary  lever  is  added  in  such  a  position  that  when 


FIG.  13. 

the  main  lever  CC  is  at  right  angles  to  the  guides  the  line  AD  will  be  at 
right  angles  to  the  cord  when  the  latter  is  led  in  the  desired  direction. 
In  all  motions  of  this  kind  there  is  a  radical  defect  due  to  the  fact 
that  while  the  cross-head  moves  in  a  straight  line  any  point  on  the  lever 
swings  through  the  arc  of  a  circle.  In  Fig.  12  let  the  line  ox  represent 
the  stroke  of  an  engine.  A  lever  attached  to  the  cross-head  and  suitably 
suspended  at  the  other  end  would  take,  as  the  stroke  progressed,  the 
positions  1  1',  2  2',  3  3',  etc.,  and  a  pin  attached  to  the  lever  at  1'  would 
move  through  the  arc  shown.  Divide  the  stroke  into  eight  equal  parts, 
as  indicated  by  the  numbered  divisions,  and  as  the  cross-head  completes 
each  division  of  the  stroke  the  position  of  the  pin  will  be  indicated  by 


REDUCING   MOTION 


15 


the  corresponding  number  upon  the  arc.  The  length  of  the  diagram 
will  be  the  horizontal  distance,  between  I'  and  9',  but  the  distribution 
of  motion  between  these  points  will  not  be  equal  for  equal  movements 
of  the  cross-head.  When  the  cross-head  moves  from  1  to  2,  one-eighth 
of  the  stroke,  the  pin  will  move  from  1'  to  2,'  and  the  cord  will  be  moved 
only  through  a  distance  A  a  instead  of  through  A  A'  one-eighth  of  its 
own  length;  and  for  each  division  of  the  stroke  the  proper  division  of 
the  diagram  is  indicated  by  the  full  lines,  and  the  division  that  would 
be  derived  from  the  motion  of  the  pin  by  the  dotted  lines.  Supposing 
the  cut-off  to  take  place  at  a  quarter  of  the  stroke,  this  point  should 


be  at  B,  but  would  appear  at  6,  and  the  dotted  and  incorrect  instead 
of  the  full-line  correct  diagram  would  be  drawn.  The  points  coincide 
in  the  middle  of  the  diagram,  and  become  as  much  too  late  at  the  end 
as  they  were  too  early  at  the  beginning,  the  points  which  should  be  at 
c,  d,  and  e  being  at  c',  d',  and  ef  respectively.  The  distortion  shown 
here  is  exaggerated  on  account  of  the  shortness  of  the  lever.  It  decreases 
as  the  length  of  the  lever  in  proportion  to  the  stroke  is  increased,  and 
for  this  reason  it  is  advisable  never  to  use  a  lever  less  than  one  and  a 
half  times  the  length  of  the  stroke.  The  point  of  suspension  of  the  lever 
should  be  directly  over  its  point  of  attachment  to  the  cross-head  when 
thd  latter  is  in  the  center  of  its  stroke. 


16  THE   STEAM   ENGINE   INDICATOR 

The  amount  of  distortion  varies  also  with  the  manner  of  attachment 
to  the  cross-head.  Fig.  13  represents  a  slotted  lever  working  over  a  pin 
in  the  cross-head.  As  each  eighth  of  the  stroke  is  completed  the  lever 
will  occupy  the  positions  shown  by  the  lines  passing  from  the  point  of 
suspension  through  the  corresponding  divisions,  and  the  straight  motion, 
as  AB,  to  be  derived  from  any  point  upon  the  lever  will  be  unequally 
divided,  as  shown  by  the  intersections  of  the  dotted  lines.  Fig.  14 
represents  a  lever  fitted  with  a  pin,  which  is  carried  by  a  slot  in  the 
cross-head.  As  the  cross-head  and  the  slot  move  through  successive 
eighths  of  the  stroke,  the  pin  is  carried  also  through  equal  divisions, 
and  motion  in  a  line  CD,  at  right  angles  to  the  lever  in  its  central  position 
would  be  equally  distributed,  as  shown  by  the -intersections  of  the  dotted 
lines  referring  the  positions  of  the  pin  for  the  eight  equal  divisions  of 
the  stroke  to  the  line  of  motion  CD.  If  it  were  not  for  the  angular  move- 
ment of  the  cord  with  which  this  motion  is  taken  off,  and  which  pro- 
duces an  inequality  in  the  transmitted  motion,  just  as  a  connecting  rod 
does  in  the  travel  of  the  piston  for  equal  movements  of  the  crank,  this 
arrangement  would  be  perfectly  accurate.  The  cord  is  usually  so  long, 
however,  that  its  angular  motion  is  immaterial.  This  feature  cannot 
be  eliminated  by  using  the  arc  or  brumbo  pulley,  for  while  the  latter 
disposes  of  the  angular  movement  of  the  string,  it  gives  a  movement 
proportional  to  the  angular  motion  of  the  lever,  which  is  not  equally 
divided,  i.e.,  the  lever  does  not  move  through  equal  arcs  of  a  circle  for 
equal  movements  of  the  cross-head.  The  use  of  the  brumbo  in  this 
case  would  therefore  introduce  rather  than  eliminate  an  error.  While 
this  arrangement  produces  upon  paper  an  almost  perfectly  proportional 
reduction  of  the  motion,  its  effects  in  practice  are  not  so  precise.  The 
long  lever  is  cumbersome,  the  slotted  guide  an  awkward  thing  to  make 
and  attach  to  the  cross-head,  and  unless  the  pin  is  accurately  fitted, 
the  distortion  and  annoyance  due  to  lost  motion  will 
be  greater  than  the  inherent  error  of  simpler  construc- 
tion. 

Instead  of  the  slot  upon  the  cross-head  a  short  con- 
nection rod  may  be  used,  as  in  Fig.  15.     In  this  case  the 
end  of  the  main  lever,  instead  of  working  up  and  down 
j  in  a  vertical  slot,  is  swung  in  the  arc  of  a  circle  of  the 

radius  of  the  short  connecting  rod.    The  departure  from 
__—--'    the   vertical  line  will  be  least  if  the  levers  are  so  at- 
rj~"  tached  that  the  vibrating  end  of  the  small  lever  will 

FIG.  15.  be  as  much  ^elow  the  path  of  the  cross-head  end  when 

the  main  lever  is  in  its  central  position  as  it  is  above 
it  when  in  the  extreme  positions.  This  will  be  understood  by  referring 
to  Fig.  16,  in  which  the  levers  are  represented  by  the  lines  A B  and  BC, 


REDUCING  MOTION 


17 


the  cross-head  traveling  on  the  line  numbered  0  to  8.  When  the  cross- 
head  is  in  the  middle  of  its  stroke  at  4,  the  ends  B  of  the  levers  are 
as  much  below  the  line  in  which  the  cross-head  travels  as  they  are 
above  it  in  the  extreme  position  shown  at  B'  and  6.  When  the  cross- 


FIG.  16 


\ 


0 


<C 

/ 

/ 
/ 
i 

\ 

/'* 

\ 

•*^ 

**s 

^"•\    o' 

:::^5;^3J_.__B 

_41_       Zg^S^ZSL- 

rtr  

Co]            i 

f*                31               4 

5 

i       i 

j          i 

• 

FIG.  17. 


head  in  its  movement  arrived  at  the  points  1,  2,  3,  etc.,  representing 
equal  subdivisions  of  its  travel,  the  ends  of  the  levers  would  be  respect- 
ively at  the  figures  1',  2',  3',  etc.,  crossing  the  line  of  motion  of  the 
cross-head  twice  during  the  stroke.  Referring  these  points  to  the  straight 
line,  OX  by  the  dotted  lines,  it  will  be  seen  that  the  subdivisions  very 


18 


THE   STEAM   ENGINE   INDICATOR 


nearly  reproduce  the  equal  subdivisions  of  the  movement  of  the  cross- 
head  from  they  are  derived. 

If  the  levers  had  been  arranged  at  a  right  angle  when  in  the  center 
of  the  stroke,  as  in  Fig.  17,  the  entire  vibration  of  the  levers  would 
take  place  above  the  plane  in  which  the  cross-head  moves..  The  greater 
distance  to  which  the  end  of  the  small  lever  is  carried  from  that  plane 


FIG.  18. 


would  increase  the  angle  between  them  and  introduce  a  greater  dis- 
tortion, as  will  be  seen  from  Fig.  17,  in  which  the  same  process  has 
been  carried  out  as  in  Fig.  16,  the  movement  derived  from  any  point  in 
the  main  lever  being  represented  by  the  subdivisions  into  which  the 
dotted  lines  divide,  the  line  OX,  which  as  will  be  seen,  are  far  more 
irregular  than  in  Fig.  16. 

The    Pantograph. — Engravers    and    draftsmen    have    an    instrument 
called-  the    "  pantograph  ^    for   reproducing    drawings    upon    a    different 

scale.     One  of  the  cheaper  forms  of  the 
A       instrument    is    shown   in    Fig.    18.       A 
/'I       drawing  followed  with  the  tracing  point 
'         is  reproduced  upon   a   smaller   scale   by 
/          the    pencil    point,    as    shown.       If    the 
/  tracing   point   draws   a  circle  the  pencil 

/  draws    a    smaller  circle;    if   the    tracing 

/  point  draws    a    straight    line  the   pencil 

/  point  draws  a  shorter  straight  line,  and 

the  movement  of    the  pencil  point  and 
tracing    point  are  proportional  through- 
/"*         out.     When  the  tracing  point  has  drawn 
one-tenth  of  its  line  the  pencil  has  drawn 
one-tenth  of  its  line  and  so  on  to  com- 
FIG.  19.  pletion.     It  "will  readily  be   seen  that  if 

the  tracing  point   of  the  pantograph  be 

attached  to  an  engine  cross-head  the  pencil  will  accurately  reproduce  the 
stroke  upon  a  reduced  scale,  and  substituting  a  cord  pin  for  the  pencil  we 


REDUCING  MOTION 


19 


have  a  perfect  reproduction  of  the  motion  of  the  cross-head  for  trans- 
mission to  the  paper-barrel.  The  two  forms  in  which  the  pantograph  is 
used  for  indicator  purposes  are  shown  in  Figs.  19  and  20.  Of  both  forms 
it  is  true  that  the  cord  pin  C  must  be  directly  in  line  with  the  stationary 
point  A  and  the  point  of  attachment  to  the  cross-head  B,  as  indicated 
by  the  dotted  lines;  also  that  the  distance  from  the  point  of  suspension 
A  to  the  cord  pin  C  is  to  the  distance  between  A  and  B  as  the  length 
of  the  diagram  is  to  the  stroke  of  the  engine,  so  that  the  rules  given  for 
the  lever  will  apply  equally  well  to  the  pantograph.  The  distance  AC 
may  be  varied  by  moving  the  strip  C  to  one  or  another  of  the  holes  1, 
2,  3,  etc.,  and  then  moving  the  cord  pin  into  that  hole  in  the  strip  which 
is  in  the  center  line  of  the  instrument.  The  author  has  pasted  into  the 
cover  of  his  indicator  box  the  following  table,  correat  for  the  pantograph 
which  he  uses,  which  is  like  Fig.  20. 

PANTOGRAPH  TABLE 


Hole. 
No. 

Proportion  Card 
to  Stroke. 

Decimal  Fraction 
of  Stroke. 

Divided 
by 

Longest 
Stroke. 

1 

1:16 

.0625 

16 

72' 

2 

1:12 

.0833 

12 

54' 

3 

5:48 

.1042 

9.6 

42' 

4 

1:   8 

.1250 

8 

36' 

5 

7:48 

.1458 

6.9 

31' 

6 

1:   6 

.1667 

6 

27' 

7 

3:16 

.1875 

5.3 

24' 

8 

5:24 

.2083 

4.8 

22' 

9 

11:48 

.2292 

4.4 

20' 

10 

1:   4 

.2500 

4 

18" 

11 

13:48 

.2836 

3.7 

16" 

This  shows  that  when  the  pin  is  in  the  first  hole  (No.  1)  the  diagram 
will  be  one-sixteenth  or  0.0625  of  the  length  of  the  stroke;  in  the  fifth 
hole  seven  forty-eighths,  or  0.1458,  etc.  To  find  the  movement  of  the 
cord  pin  at  any  hole  with  an  engine  of  given  stroke,  multiply  the  stroke 
in  inches  by  the  decimal  fraction  opposite  the  number  of  hole  given; 
or  divide  the  stroke  in  inches  by  the  number  in  the  column  headed 
"divided  by"  opposite  the  number  of  the  hole  given. 

To  find  the  proper  hole  to  use  with  an  engine  of  given  stroke  to  pro- 
duce a  diagram  of  a  required  length:  Divide  the  length  of  the  stroke 
in  inches  by  the  desired  length  of  diagram  in  inches.  The  number  nearest 
to  the  quotient  in  the  column  headed  " divided  by"  will  be  opposite 
the  number  of  the  hole  which  will  nearest  produce  that  length.  The 
ratio  of  the  diagram  to  the  stroke  may  coincide  with  one  of  those  given 
in  the  table.  Thus,  if  it  was  desired  to  produce  a  four-inch  diagram 


20 


THE   STEAM   ENGINE   INDICATOR 


from  a  thirty-two-inch  stroke,  the  ratio  would  be  4:32=1:8,  and  it  is 
apparent  from  the  columns  of  proportions  given  that  the  pin  in  the 
fourth  hole  will  have  the  required  movement.  The  same  result  may 
be  arrived  at  by  dividing  the  length  of  the  diagram  in  inches  by  the 
stroke  in  inches  and  selecting  the  pinhole  which  is  opposite  the  nearest 
decimal  fraction  to  that  obtained.  The  last  column  of  the  table  gives 
the  longest  strokes  allowable  for  the  various  positions  of  the  pin  to  pro- 
duce diagrams  not  exceeding  four  and  a  half  inches  in  length,  which 
is  about  the  capacity  of  the  ordinary  drum.  Additional  columns  for 


FIG.  20. 

other  lengths  may  be  made  out  if  desired  by  multiplying  the  figures  in 
the  column  headed  " divided  by"  by  the  length  of  diagram  desired. 
Such  a  column,  for  instance,  might  be  added  for  the  maximum  length 
of  diagram  allowable  with  the  smaller  drum,  although  the  smaller  in- 
struments are  usually  used  upon  engines  of  high  rotative  speeds,  where 
the  pantograph  is  not  adapted  as  a  reducing  motion. 

In  the  other  form  of  pantograph,  Fig.  19,  holes  are  provided  for  dif- 
ferent positions  of  the  strip  C,  and  other  holes  in  C  for  bringing  the  cord 
pin  in  line  with  A  and  B.  Other  holes  are  sometimes  provided  for  chang- 
ing the  point  of  attachment  to  the  cross-head,  in  which  case  the  cord 
pin  must  always  be  in  line  with  the  stationary  point  A  and  the  hole 
which  is  used  for  the  cross-head  attachment,  and  the  length  of  the  diagram 
will  be  to  the  length  of  the  stroke  as  AC  is  to  A  B. 


REDUCING   MOTION 


21 


In  view  of  this  latter  fact,  if  the  pantograph  is  opened  until  AB 
equals  the  stroke  of  the  engine,  then  AC  will  be  the  length  of  the  diagram 
at  once,  and  with  the  shorter  strokes  this  fact  may  be  used  to  advantage 
in  setting  the  pantograph.  Suppose  the  stroke  to  be  24  inches.  Open 
the  pantograph  until  a  two-foot  rule  wrill  just  extend  from  center  to 
center  of  pins  A  and  B,  as  in  Fig.  21,  then  the  distance  C  to  A  will  be 
the  length  of  diagram  to  be  expected,  and  the  pin  may  be  so  adjusted 
as  to  make  this  distance  equal  to  the  length  of  diagram  desired.  For 
greater  lengths  of  stroke  this  principle  may  still  be  used  by  halving. 
Take  a  72-inch  stroke,  for  instance.  One-half  of  this  is  three  feet.  Qpen 
the  pantograph  to  three  feet,  then  the  distance  AC  will  equal  one-half 
the  length  of  the  diagram. 

There  is  no  patent  upon  the  pantograph  in  either  of  these  forms, 
and  anybody  who  has  tools  and  know^s  how  to  use  them  can  make  for  one 


FIG.  21. 


FIG.  22. 


himself.  The  members  are  usually  made  of  strips  of  hard  wood  one  and 
one-eighth  by  five-sixteenths  of  an  inch,  and  sixteen  inches  between 
the  pivoted  points.  These  strips  are  put  together  in  the  manner  indi- 
cated in  the  illustration,  the  single  strips  running  between  the  double 
making  it  stiff  and  substantial.  The  levers  must  work  easily,  and  all 
lost  motion  be  avoided.  The  joints  must  be  well  made  and  the  pivot 
holes  should  be  bushed.  A  good  form  of  joint,  designed  by  Mr.  E.  K. 
Conover,  is  shown  in  Fig.  22.  It  allows  for  taking  up  lost  motion  by 
filing  off  the  bush,  and  permits  the  bearing  to  be  taken  apart  and  oiled 
occasionally.  The  holes  which  are  used  for  the  different  positions  of 
the  strip  and  of  the  cord  pin  are  usually  tapped  directly  into  the  wood, 
but  the  tops  are  apt  to  be  forced  out  or  the  threads  crossed  and  cut,  and 
a  better  arrangement  would  be  to  insert  strips  of  brass  at  these  places, 
and  drill  and  tap  the  holes  into  them. 

So  far  as  the  correctness  of  the  reduction  goes  it  makes  no  difference 
where  the  stationary  end  of  the  pantograph  is  placed.  We  have  seen 
engineers  measure  with  a  great  deal  of  care  to  locate  this  point  accurately 
in  the  center  of  the  stroke,  knowing  probably  that  this  had  to  be  done 


22 


THE   STEAM   ENGINE   INDICATOR 


for  the  lever  and  assuming  that  the  pantograph  required  similar  arrange- 
ment. The  cord,  of  course,  should  be  led  off  in  the  line  of  rnotion  of  the 
pin,  i.e.,  parallel  to  the  guides,  and,  since  it  is  desirable  to  dispense 
with  the  use  of  leading  pulleys,  when  the  pantograph  is  used  horizon- 
tally, as  in  Fig.  23,  the  post  should  be  placed  at  such  a  distance  from  the 
guides  and  at  such  a  height  as  will  bring  the  cord  pin  directly  in  line 
with  the  indicators,  so  that  the  cord  can  be  led  direct  as  shown  in  the 
plan.  The  point  to  be  looked  out  for  is  that  the  corners  A  and  B  of  the 
pantograph  do  not  come  in  contact  with  the  guides  at  the  extremes  of 
the  itroke.  We  have  seen  several  good  pantographs  spoiled  in  that  way, 
and  plead  guilty  to  one  wreck  ourselves  from  that  cause.  Now  we  try 
it  by  having  the  engine  turned  over,  if  this  can  be  done  easily,  while 
holding  the  stationary  end  of  the  pantograph,  moving  it,  if  it  hits,  into 
a  position  in  which  it  will  clear;  or  if  the  engine  is  a  large  one,  by  locating 
the  extreme  points  of  the  pantograph's  travel  by  measurement,  and  carry- 
ing the  cross-head  end  through  the  range  so  determined  in  as  nearly 


as  possible  the  line  that  it  will  travel,  observing  that  it  clears  through- 
out the  stroke.  When  the  pantograph  is  all  attached  and  running, 
place  your  eye  at  C  and  sight  the  cord  pin.  It  should  move  in  a  straight 
line  to  and  from  your  eye.  If  it  has  any  side  wise  motion  something  is 
wrong;  probably  the  pin  is  not  in  the  center  line  of  the  instrument.  The 
stationary  post  will  come  about  in  the  middle  of  the  guide,  with  this 
arrangement,  as  if  moved  much  to  either  end  it  will  bring  the  corner  at 
that  end  in  contact. 

Remembering  that  it  makes  no  difference  how  the  pantograph  is 
set,  horizontally,  perpendicularly,  or  obliquely,  so  long  as  it  will  clear, 
it  may  be  placed  in  any  position  to  favor  leading  the  cord  to  the  indicators. 
Fig.  24  shows  how  it  may  be  used  on  an  engine  whose  stroke  does  not 
exceed  the  length  to  which  the  pantograph  may  be  easily  opened.  The 
other  form  of  pantograph  may  be  attached  to  the  floor,  as  in  Fig.  25, 
in  which  case  a  leading  pulley  is  required,  but  where  the  stroke  of  the 
engine  will  allow  it  had  better  be  attached  as  in  Figs.  26  and  27. 

Fig.  28,  from  the  catalogue  of  the  Buckeye  Engine  Co.,  shows  an 
adaptation  of  the  pantograph  for  that  engine.  The  cord  is  attached 


REDUCING   MOTION 


23 


to  the  end  of  a  short  bar  which  slides  freely  in  a  bearing  in  the  carrying 
post.  This  bar  is  connected  to  the  lever  CD  by  means  of  a  short  link 
AB.  The  lever  is  connected  to  a  stud  attached  to  the  cross-head  at  E 
by  the  bar  DE.  The  proportions  of  the  parts  are  such  that  the  points 


FIG.  24. 


FIG.  25. 


CBE  are  in  a  straight  line  at  all  times,  and  this  being  the  case  the 
distortions  of  the  movement  of  the  lever  due  to  the  vibration  of  the 
link  DE  will  be  corrected  by  the  equal  vibration  of  the  short  link.  This 
makes  a  good  rig  for  a  permanent  fixture,  but  must  be  proportioned 


FIG.  26. 


FIG.  27. 


for  the  engine  upon  which  it  is  used,  as  it  cannot,  except  within  very 
narrow  limits,  be  adjusted  for  engines  of  different  sizes.  The  cord  must, 
of  course,  be  led  off  in  the  line  of  motion  of  the  short  bar. 


24 


THE  STEAM   ENGINE   INDICATOR 


Fig.  29  shows  a  very  good  motion  for  short  strokes.  The  amount 
of  motion  given  to  the  bell  crank  may  be  varied  by  changing  the  inclina- 
tion of  the  plane  which  is  attached  to  the  cross-head,  and  the  vertical 
arm  may  be  of  such  length  as  to  bring  the  cord  in  line  with  the  indicator. 


FIG.  28. 

The  catch  C  holds  the  foot  up  off  the  plane  and  stops  the  instrument 
without  unhooking  the  cord  or  leaving  it  flapping  as  with  a  detent  on  the 
indicator  drum. 

Fig.  30  shows  a  method  of  reducing  the  motion  by  means  of  wheels 
or  sheaves  of  different  diameters. 


FIG.  29. 


A  standard  upon  the  cross-head  is  clamped  at  c  to  a  cord  which  passes 
around  the  pulleys  W  and  w,  the  hub  H,  from  which  motion  is  taken 
to  the  indicator,  bearing  the  same  proportion  to  the  wheel  W  that  the 
length  of  diagram  is  to  bear  to  the  stroke.  This  arrangement  has  the 


OF  THE 

UNIVERSITY 

OF 

jdUFOR! 


REDUCING  MOTION 


25 


advantage  that  the  wheel  W  is  kept  in  time  with  the  piston  by  being 
held  from  overturning  through  momentum  by  the  cord.  Another 
cord  can  be  led  from  H  to  the  indicator  upon  the  back  end  of  the  cylinder. 
The  trouble  with  those  reducing  wheels  which  are  pulled  out  by  the  cord 
and  returned  by  means  of  a  spring  has  been  that  having  considerable 
mass  they  acquired  a  momentum  which  carried  them  after  the  cross- 
head  had  stopped  pulling,  and  distorted  the  stroke,  like  a  heavy  paper- 
barrel  with  a  weak  drum  spring  on  an  indicator  at  high  speed.  Several 


w  ft- 


S 


FIG.  30. 


forms  of  reducing  wheels  are  now  upon  the  market,  however,  in  which 
lightness  of  material  and  construction  have  combined  to  form  a  device 
which  is  not  only  handy  in  application  to  different  sizes  and  kinds  of 
engines,  but  reasonably  accurate  at  considerable  speeds.  Finally,  what- 
ever form  of  motion  is  used,  there  are  two  tests  which  should  be  tried. 
The  first  of  these  is  shown  in  Fig.  31,  where  the  stroke  of  the  cross-head 
is  divided  into  eight  equal  parts.  With  the  reducing  motion  attached  to 
the  indicator,  put  the  engine  on  the  center,  the  corner  A  of  the  cross- 
head  being  at  zero.  In  this  position  make  a  vertical  mark  upon  the 
indicator  card  by  raising  the  pencil  lever.  Then  move  the  cross-head 


26 


THE  STEAM  ENGINE   INDICATOR 


successively  to  1,  2,  3,  etc.,  at  each  point  making  a  mark  upon  the  card. 
If  the  diagram  is  found  to  be  equally  spaced  your  motion  is  correct  so 
far  as  the  reduction  is  concerned.  Now  give  the  engine  steam,  and  while 
it  is  turning  over  slowly  apply  the  pencil,  and  hold  it  on  during  a  complete 
revolution,  making  an  "  atmospheric "  line.  Raise  the  pencil  about 


FIG.  31, 


a  sixteenth  of  an  inch,  let  the  engine  get  up  to  speed,  and  draw  another 
line  in  the  same  way.  If  there  is  a  considerable  difference  in  the  length 
the  diagram  will  be  distorted  by  the  momentum  of  the  reducing  motion, 
or  of  the  paper-drum  of  the  indicator  itself,  or  by  the  stretching  of  the 
cord.  The  most  that  you  can  do  is  to  take  up  all  lost  motion,  use  short 
cord  or  wire,  and  adjust  the  drum  spring  to  get  the  least  possible  dis- 
crepancy. 


CHAPTER  III 
APPLICATION 

HAVING  selected  an  instrument  and  laid  out  an  appropriate  reduc- 
ing motion,  we  are  prepared  to  consider  the  attachment  of  the  indicator 
to  the  cylinder  and  the  method  of  its  manipulation. 

Most  engines  of  recent  build  are  sent  out  of  the  shop  with  the  cylinder 
drilled  and  tapped  for  the  application  of  the  indicator,  and  plugged  holes 
for  this  purpose  will  be  found  in  the  side  or  top  of  the  cylinder  by  remov- 
ing the  lagging.  When  a  cylinder  is  not  tapped,  the  two  points  to  be 
considered  in  locating  the  point  for  drilling  are,  first,  to  so  place  the  hole 
that  throughout  the  stroke  there  shall  be  a  constant  uninterrupted 
communication  between  the  cylinders  of  the  indicator  and  the  engine; 
and  secondly,  to  so  locate  the  instrument  as  to  lead  off  from  it  most 
conveniently  to  the  reducing  motion. 

The  first  object  is  most  readily  attained  by  tapping  directly  into 
the  heads,  and  as  this  is  rather  a  more  simple  process  for  the  machinist 
than  tapping  into  the  counter-bore,  especially  when  room  is  limited, 
it  is  frequently  done.  Except  in  a  few  instances,  however,  as  in  working 
from  the  crank  end  of  an  upright  cylinder,  it  brings  the  instrument  out 
of  easy  reach  of  the  line  from  the  reducing  motion,  and  this  line  should 
be  kept  as  short  and  direct  as  possible.  The  most  advantageous  method 
of  connection  will  usually  be  found  to  be  by  tapping  through  the 
cylinder  wall  into  the  counter-bore,  as  at  A,  Fig.  32.  Whether  this  will 
be  at  the  side  as  in  Fig.  34,  or  top  as  in  Fig.  33,  of  the  cylinder  will 
depend  upon  the  location  of  the  steam  chest  and  the  direction  of  the 
cord.  Usually  in  the  larger  engines  with  vertical  cross-head  the  indicators 
are  most  conveniently  located  at  the  side,  while  in  the  small  self-con- 
tained engines,  with  horizontal  cross-head,  the  indicator  is  most  accessible 
on  top  of  the  cylinder. 

Having  determined  where  the  indicator  is  to  be  located,  drill  and 
tap  the  cylinder  for  a  half-inch  pipe  thread,  being  careful  to  see  that  the 
hole  is  not  covered  by  the  piston,  but  that  it  is  in  free  communication 
with  the  cylinder  at  all  points  of  the  stroke.  When  the  counter-bore 
is  too  close  and  the  clearance  small,  access  may  be  had  by  chipping  a 
channel  from  the  tapped  hole  out  into  the  clearance.  Of  course  every 

27 


28 


THE   STEAM   ENGINE   INDICATOR 


attention  should  be  paid  to  cleaning  out  chips  and  borings  so  that  the 
cylinder  may  not  be  cut  nor  the  indicator  injured. 

Into  the  hole  so  prepared,  screw  the  indicator  cock  direct  whenever 
possible.  When  the  cylinder  is  tapped  upon  the  side,  this  will  bring 
the  instrument  horizontal,  as  in  Fig.  34,  but  the  author  much  prefers 
this  arrangement  to  the  more  common  one  shown  in  Fig.  35,  where  a 
nipple  and  elbow  are  used  to  bring  the  indicator  into  a  vertical  position. 
The  shorter .  and  more  direct  the  connection  between  the  cylinder  of 
the  indicator  and  the  engine,  the  more  accurate  will  be  the  results,  and 
it  must  be  remembered  that  all  the  pipes  and  connections  to  be  rilled 


FIG.  32. 

with  steam  represent  so  much   added   clearance  to  the  engine,   which 
on  a  small  machine  might  amount  to  a  considerable  percentage. 

In  all  cases  where  accuracy  is  important,  a  pair  of  instruments  should 
be  used,  one  on  each  end  of  the  cylinder,  and  diagrams  taken  simul- 
taneously. Where  only  one  indicator  is  available  it  is  more  convenient 
to  attach  it  to  a  three-way  cock  connected  with  both  ends  of  the  cylinder, 
so  that  it  may  be  thrown  into  communication,  first  with  one  end  and 
then  the  other,  as  at  Fig.  36.  This  method  cannot  be  depended  upon 
for  accuracy,  however,  and  no  important  changes  or  deductions  which 
could  be  affected  by  the  intermediate  connections  should  be  made  from 
the  indications  of  an  instrument  attached  in  that  way.  Its  convenience, 
however,  will  lead  to  its  continued  use  in  cases  where  a  single  instru- 
ment is  in  frequent  use  upon  the  same  engine;  and  if  proper  allowance 


APPLICATION 


29 


is  made  for  the  distortions  produced  by  wire  drawing  and  clearance,  no 
harm  will  result. 

A  proper  precaution  is  to  take  a  diagram  with  the  indicator  attached 
directly  to  the  cylinder,  and  then  take  another  through  the  three-way 
cock,  under  as  nearly  as  possible  the  same  conditions,  upon  the  same 
paper.  This  will  enable  you  to  make  an  intelligent  estimate  of  the 
difference  due  to  the  different  methods  of  connection.  We  have  seen 
diagrams  taken  with  the  three-way  cock  which  could  scarcely  be  dis- 
tinguished from  those  taken  with  the  direct  connection,  while  others 
have  shown  distortions  which  utterly  unfitted  them  as  indications  of 


FIG.  33. 

the  action  of  steam  in  the  cylinder.*  The  side  pipes,  when  used,  should 
be  ample  in  size  to  convey  the  steam  to  the  indicator  without  wire- 
drawing, but  not  any  larger  than  necessary,  on  account  of  the  increase 
in  clearance. 

The  method  of  connection  shown  in  Fig.  37  is  especially  to  be 
avoided.  Here  angle  valves  are  attached  to  the  ends  of  the  cylinder 
and  connected  with  a  side  pipe,  in  the  center  of  which  is  a  T  for  the 
insertion  of  the  indicator  cock.  To  connect  the  indicator  with  either 
end  of  the  cylinder,  the  angle  valve  at  that  end  is  opened,  the  valve 
at  the  other  end  being  closed.  It  is  evident  that  in  order  to  get  any 

*  See  Chapter  on  Errors  in  the  diagram. 


30 


THE   STEAM   ENGINE   INDICATOR 


pressure  to  the  indicator  the  entire  length  of  the  side  pipe  must  first 
be  filled  with  steam  at  each  stroke;  and  for  every  reason  that  the 
ordinary  side  pipe  is  bad,  this  is  twice  as  bad.  There  is  also  no  know- 


FIG.  34. 


ing  whether  the  valve  which  is  supposed  to  be  shut  is  tight,  or  whether 
it  is  entirely  closed  every  time.  Should  it  remain  slightly  open,  as 
is  frequently  the  case  even  when  a  valve  feels-  tight,  some  unaccountable 


FIG.  35. 


effects  may  appear  in  the  lines  of  the  diagram  taken  supposedly  from 
the  other  end  alone. 

In  putting  up  piping  or  connections  for  use  with  the  indicator,  use 
no  red  lead  or  other  mixture,  as  it  will  be  carried  by  the  steam  to  the 


APPLICATION 


31 


indicator  cylinder  and  produce  trouble  by  sticking  the  piston  up.  A 
few  drops  of  oil  on  the  thread  is  usually  all  that  is  required,  but  should 
a  joint  persist  in  leaking,  a  string  of  waste  wound  in  the  thread  will 
make  it  tight. 

Particular  pains  should  be  taken  to  remove  from  all  pipes  and 
fittings  all  dirt,  scale,  and  burr  which  can  become  detached  and  work 
into  the  cylinder.  A  little  piece  of  grit  upon  the  indicator  piston  can 
cut  some  funny  freaks  upon  the  paper-barrel,  as  well  as  leave  its  mark 
upon  the  walls  of  the  indicator  cylinder.  When  the  connections  are  all 
up,  allow  the  steam  to  blow  through  them  freely  some  time  before  attach- 
ing the  instrument,  rapping  the  pipe  sharply  in  the  meantime,  to  remove 
any  scale  or  dirt  which  is  liable  to  become  detached. 


FIG.  36. 


The  cylinder  having  been  tapped  and  the  reducing  motion  arranged, 
we  are  now  ready  to  apply  the  indicator  to  the  cylinder;  and  here  is 
where  we  begin  to  appreciate  the  fallacy  of  making  indicators  in  pairs 
right  and  left,  for  if  one  is  right  for  the  side  of  the  engine  you  are  upon, 
the  other  is  certainly  wrong.  You  are  bound  to  want  either  two  right- 
hand  indicators  or  two  left-hand  indicators  at  the  same  time,  and  when 
the  makers  recognize  this  and  make  their  instruments  so  they  can  be 
changed  from  right  to  left,  there  will  be  fewer  burnt  knuckles  and  less 
profanity  connected  with  the  use  of  the  indicator.  The  owner  can 
adapt  his  instrument  to  the  change  by  simply  filing  a  slot  in  the  bottom 
of  the  barrel  opposite  the  present  slot,  so  that  the  clips  and  pencil  bar 
may  be  brought  to  that  side  of  the  instrument  which  is  away  from  the 
cylinder  when  in  use. 


32 


THE   STEAM   ENGINE   INDICATOR 


Do  not  undertake  to  turn  the  instrument  backwards  to  bring  the 
clips  on  the  outside,  but  in  putting  the  instrument  upon  the  cock,  let 
the  arm  which  holds  the  barrel  point  in  the  direction  which  the  string 
is  to  lead.  It  is  better  to  take  off  the  working  parts  of  the  instrument 
and  leave  them  in  the  box  while  doing  this,  avoiding  the  risk  of  bending 
the  levers  and  connections  in  handling,  or  catching  them  on  the  cord 
while  rigging  up.  Put  a  little  waste  in  the  cylinder  meanwhile. 

A  good  idea  for  one  who  used  his  indicators  a  good  deal  and  in  dif- 
ferent places  would  be  to  have  duplicate  cylinder  caps  without  holes. 
The  regular  cap  with  the  attached  pencil  motion  and  piston  could  then 
be  replaced  by  the  solid  cap  while  rigging  up,  saving  the  delicate  parts 
of  the  instrument  from  possible  harm  and  keeping  the  cylinder,  upon 


FIG.  37. 

the  perfection  of  the  inside  surface  of  which  so  much  depends,  shut  up 
tightly. 

The  connection  between  the  paper-barrel  and  the  reducing  motion 
may  be  made  with  a 'flexible  cord,  as  the  drum  is  rotated  in  one  direc- 
tion by  a  spring.  It  has  already  been  explained  that  in  order  to  secure 
a  distribution  of  the  pressure  on  the  diagram  corresponding  to  the  dis- 
tribution in  the  cylinder,  it  is  essential  that  the  paper-drum  shall  correspond 
in  its  movement  with  the  movement  of  the  piston.  To  secure  this,  even 
with  a  correct  reducing  motion,  it  is  essential  that  there  shall  be  no 
stretch  in  the  cord  which  forms  the  connection,  through  the  reducing 
motion  and  cross-head,  with  the  piston. 

If  the  engine  piston  has  to  move  an  inch  before  the  stretch  is  taken 
out  of  the  cord  sufficiently  to  enable  it  to  start  the  drum,  it  is  evident 
that  the  admission  end  of  the  diagram  produced  will  not  present  correctly 


APPLICATION  33 

the  action  of  the  steam  with  reference  to  the  beginning  of  the  stroke. 
The  distortions  produced  will  be  explained  in  a  chapter  devoted  to  the 
errors  to  which  the  diagram  is  liable*  It  is  enough  now  to  appreciate 
that  no  stretch  is  allowable  if  accurate  work  is  to  be  done. 

A  closely  braided  cord,  prepared  especially  for  indicating  purposes, 
is  supplied  by  dealers  in  the  instruments.  It  is  well  to  hang  a  weight 
upon  this  cord,  and  allow  it  to  remain  suspended  some  time  before  using, 
to  take  out  any  tendency  to  stretch  which  may  remain  in  it. 

Where  the  distance  from  the  indicator  is  considerable,  as  in  the  case 
of  a  Corliss  engine,  with  the  pantograph  in  the  middle  of  the  guides, 
the  author  uses,  instead  of  a  cord,  annealed  iron  wire  of  about  22  gage. 
This  wire  is  subject  to  occasional  breakage,  but  does  not  stretch,  and  a 
dime  will  buy  enough  of  it  to  serve  for  many  applications.  It  should 
be  straightened  and  all  the  kinks  taken  out  by  being  made  fast  at  one 
end  and  wrapped  about  a  round  piece  of  wood,  such  as  a  screw-driver 
handle  or  hammer  handle,  as  shown  in  Fig.  38,  which  is  drawn  along 


FIG.  38. 

for  the  length  desired.     Braided  picture  cord  wire  of  small  size  is  also 
recommended  for  this  purpose. 

Whatever  is  used  to  lead  to  the  reducing  motion,  the  closely  braided 
cord  referred  to  will  be  used  to  run  over  pulleys  and  around  the  paper- 
drum.  Such  a  piece,  terminating  with  a  small  wire  hook,  will  be  found 
attached  to  the  instrument  when  purchased,  the  hook  being  intended 
to  engage  in  a  loop  at  the  end  of  the  cord  leading  to  the  reducing  motion. 
If  such  hook  is  used,  it  should  be  kept  as  close  to  the  instrument  as  prac- 
ticable, as  if  it  is  some  distance  out  it  is  liable  to  cause  the  line  to  vibrate 
disagreeably,  especially  when  the  speed  is  high.  When  the  distance 
from  the  indicator  to  the  reducing  motion  is  short  enough  to  make  the 
use  of  cord  advisable,  the  author  prefers  to  dispense  with  the  hook  alto- 
gether, using  a  cord  on  the  instrument  long  enough  to  loop  over  the  pin 
in  the  reducing  motion,  and  hooking  on  and  unhooking  at  that  point. 
This  gives  a  smooth,  continuous  line,  free  from  loops,  knots,  and  other 
encumbrances,  which  will  not  look  only  better  but  run  smoother,  "stay 


34 


THE   STEAM  ENGINE   INDICATOR 


put"  better  (for  knots  and  loops  are  always  giving  and  stretching  more 
or  less),  and  give  more  satisfactory  results. 

There  are  a  number  of  other  advantages  which  point  to  the  reducing 
motion  as  the  place  for  hitching  and  unhitching,  rather  than  having  a 
hook  at  the  indicator.  It  is  usually  easier  to  attach  the  cord  at  this 
point.  When  the  indicators  are  unhooked  there  is  no  attached  cord 
being  whipped  about  by  the  motion,  and  where  a  pair  of  instruments 
are  used,  the  throwing  on  or  off  of  one  loop  is  made  to  start  or  stop  the 
pair.  There  are  circumstances,  however,  where  this  is  impracticable, 
and  the  hook  near  the  indicator  must  be  used.  To  keep  the  moving 
cord  out  of  mischief  when  not  attached  to  the  indicator,  it  may  carry 
the  hook,  the  loop  being  made  in  the  indicator  cord,  and  be  hooked 


FIG.  39. 


into  an  elastic  band  attached  to  or  near  the  indicator  when  not  working 
the  paper-drum.  Another  method  is  to  attach  one  end  of  the  cord  to 
the  indicator,  as  in  Fig.  39,  leaving  it  long  enough  not  to  pull  tight  with 
the  extreme  motion,  and  looping  it  near  the  indicator  for  hooking  on. 

In  any  event,  the  end  of  the  cord  or  wire  which  goes  over  the  reduc- 
ing-motion  pin  should  be  looped,  to  permit  the  pin  to  turn  easily  within 
it,  and  not  tied  down  closely  upon  the  pin  as  by  a  slip-knot. 

The  next  step  is  to  adjust  the  length  of  the  cord  so  that  the  diagram 
may  come  in  the  center  of  the  card.  With  the  indicator  in  position  and 
the  engine  in  motion,  loop  the  cord  between  your  fingers  and  put  it 
over  the  pin  or  hook,  drawing  it  up  enough  to  set  the  paper-barrel  in 
motion  and  clear  the  stop.  Now  draw  the  cord  carefully  up  until  the 
barrel  touches  the  stop  on  the  outward  stroke,  then  let  it  slip  back  through 
your  fingers  until  it  touches  very  lightly  on  the  backward  stroke. 
Midway  between  these  two  positions  is  where  the  point  of  the  loop 
ought  to  be.  Take  back  nearly  half  as  much  cord  as  you  have  let  slip 


APPLICATION  35 

past,  tie  the  loop,  and  the  length  should  be  pretty  nearly  right.  Do 
not  throw  the  tied  loop  over  the  pin,  however,  nor  hook  it  on,  until 
you  have  first  held  it  against  the  pin  or  hook  while  the  motion  is  running 
and  made  sure  it  is  long  enough.  If  it  is  hitched  on  too  short,  some- 
thing is  bound  to  give  way.  If,  when  you  get  to  taking  diagrams,  it 
is  found  to  be  desirable  to  move  them  a  little  toward  one  end  or  the 
other  of  the  card,  this  may  be  done  by  knocking  the  indicator  around 
in  the  cock  enough  to  take  up  or  let  out  the  required  amount  of  cord. 
This  is  better  than  tying  knots  in  the  cord  to  take  it  up,  as  is  frequently 
done. 

A  device  which  may  be  used  for  adjusting  the  length  of  the  loop  if 
desired  on  slow  speeds  is  shown  in  Fig.  40.  It  may  be  made  of  a  small 
piece  of  sheet  brass,  of  sufficient  thickness  to  be  stiff,  in  which  are 
drilled  four  holes  about  a  quarter  of  an  inch  apart.  Pass  the  end  of 
the  cord  up  through  the  first  hole,  down  through  the  second,  up  through 
the  fourth,  down  through  the  third,  and  out  over  the  side  and  under 


FIG.  40. 

\ 

the  loop,  as  shown.  This  link  ma}'  be  slid  along  upon  the  cord,  lengthen- 
ing or  shortening  the  loop,  but  under  the  strain  of  the  paper-drum  spring 
it  will  remain  where  placed. 

Be  very  sure  that  the  passage  to  the  cylinder  is  free  and  that  the 
piston  does  not  even  partially  obstruct  it  at  the  end  of  the  stroke.  The 
beginning  of  the  stroke  is  when  the  indicator  makes  its  quickest  move- 
ment, and  a  choking  of  the  passage  will  produce  apparently  unaccount- 
able results.  By  throwing  a  ray  of  light  into  the  hole  tapped  for  the 
indicator  you  can  satisfy  yourself  as  to  the  directness  of  the  passage 
and  perhaps  get  a  point  as  to  evening  up  your  clearances  besides. 

The  tension  of  the  drum  or  barrel  spring  should  now  be  seen  to. 
When  the  engine  is  making  its  outward  stroke  this  drum  is  put  into 
motion,  and,  having  mass,  acquires  momentum,  so  that  when  the  piston 
arrives  at  the  end  of  its  stroke  and  the  string  stops  pulling,  the  drum 
continues  to  move  by  reason  of  its  momentum  until  its  stored  energy 
is  absorbed  by  the  spring.  If  a  high-speed  engine  be  run  at  a  very 
moderate  speed  and  an  atmospheric  line  be  drawn,  then  with  the  engine 
running  at  governor  speed  if  another  line  be  drawn  just  above  it,  there 
will  be  found  to  be  a  difference  in  the  length  of  the  lines.  This  produces 


36  THE  STEAM  ENGINE   INDICATOR 

a  distortion  in  the  diagram,  of  course,  and  can  be  reduced  by  tighten- 
ing the  barrel  spring.  For  high-speed  engines  this  spring  will  have  to 
be  kept  under  considerable  tension,  but  on  slower  moving  machines 
it  may  be  let  down,  and  should  in  all  cases  be  run  only  tight  enough 
to  keep  the  barrel  well  under  the  control  of  the  cord. 

The  working  parts  are  now  to  be  arranged  and  the  instrument  put 
together.  The  pencil  lever  must  be  fitted  with  a  lead.  Do  not  use 
any  more  lead  than  is  necessary  to  hold  firmly  in  the  quill  or  stub. 
Any  extra  weight  is  especially  to  be  avoided  at  this  point,  where  it  has 
so  much  motion,  and  if  allowed  to  stick  out  on  the  barrel  side  of  the 
arm  it  furnishes  a  lever  to  work  itself  loose  in  the  holder  or  to  twist 
the  pencil  arm  sideways  in  its  bearings.  Bring  the  lead  to  a  fine  round 
point,  not  sharp  enough  to  catch  in  and  scratch  the  paper.  Then  let 
it  stick  through  as  little  as  possible,  leaving  a  little  stock  for  filing  up 
the  point  as  it  wears  on  the  side  toward  the  paper,  and  break  it  off 
short  at  the  other  side. 

In  selecting  a  spring,  be  sure  to  get  one  stiff  enough.  If  the  maximum 
pressures  allowable  with  the  different  springs,  as  given  by  their  several 
makers,  are  not  exceeded,  no  harm  will  result  to  the  springs  or  to  the 
instrument,  but  it  may  be  found  desirable  to  use  stiff er  springs  to  secure 
freedom  from  excessive  vibration  at  high  speeds.  Attach  the  spring 
selected  in  its  position,  being  careful  to  screw  everything  up  to  its  place, 
put  a  drop  or  two  of  cylinder  oil  on  the  piston,  open  the  cock  on  the 
indicator  and  let  the  steam  blow  once  or  twice  through  the  cylinder, 
then  put  in  the  piston  and  screw  the  instrument  together.  If  you  get 
the  cylinder  oil  from  the  can  used  about  the  engine  room,  look  at  the 
piston  after  the  oil  has  spread  around  on  it,  and  pick  off  any  specks  of 
dust  or  grit,  which  will  show  plainly  against  the  bright  brass.  If  it  is 
a  condensing  engine,  do  not  open  the  cock  when  that  end  is  exhausting, 
or  you  may  make  more  work  for  the  air-pump  than  it  can  conveniently 
handle. 

When  the  instrument  is  together,  take  hold  of  the  pencil  lightly 
and  try  the  lever  for  lost  motion.  If  it  can  be  moved  without  pulling 
at  once  on  the  spring,  take  the  instrument  apart  and  take  up  the  con- 
nections. This  point  should  be  borne  in  mind  and  looked  after  from 
time  to  time  as  the  taking  of  cards  progresses,  for  the  connections  are 
liable  to  get  loose,  and  introduce  some  very  curious  features  in  the 
diagrams.  The  cards  should  also  be  watched,  to  see  that  the  cord 
connections  do  not  stretch  so  as  to  let  the  pencil  bring  up  against  the 
clips  at  the  end  of  the  diagram. 

When  the  instrument  has  been  put  together  properly,  open  the  cock 
and  let  steam  into  it,  setting  the  piston  and  levers  in  motion,  and  press 
your  finger  lightly  on  the  top  of  the  piston  rod,  to  see  if  everything  is 


APPLICATION 


37 


working  smoothly.  If  the  least  indication  of  gritty,  scratchy  action  is 
felt,  shut  off  the  steam  at  once,  take  the  instrument  apart,  and  find 
the  cause.  If  it  runs  smoothly,  you  are  ready  to  take  a  diagram. 

The  paper  used  with  the  indicator  should  be  a  rather  heavy,  well- 
calendered,  smooth,  tough  stock,  something  that  will  stand  being  handled, 
and  over  which  the  pencil  will  pass  without  too  much  friction.  It  should 
be  cut  of  such  width  as  to  reach  nearly  to  the  top  of  the  barrel,  and  of 
a  length  about  an  inch  longer  than  the  circumference  of  the  barrel  on 
which  it  is  to  be  used.  The  beginner  will  consider  it  necessary  to  provide 
himself  with  printed  blanks,  containing  spaces  for  all  sorts  of  observa- 
tions of  the  engine,  boiler,  weather,  etc.;  but  inasmuch  as  few  of  these 


FIG.  41.    , 

observations  have  to  be  recorded  on  each  card,  and  many  of  them, 
such  as  the  dimensions  of  the  engine,  but  once  in  a  test,  he  will  as  he 
progresses  get  to  using  slips  of  plain  paper,  marking  upon  the  back  of 
each  card  such  particulars  as  are  needed  for  the  purpose  for  which  it 
is  to  be  used. 

The  paper  is  put  upon  the  barrel  by  placing  the  lower  right-hand 
corner  under  the  longest  clip,  bending  it  around,  and  allowing  the  ends 
to  stick  out  between  the  clips  at  the  top;  then  by  taking  the  lower 
corners  as  they  protrude  between  the  clips  between  the  thumb  and 
forefinger,  as  shown  in  Fig.  41  and  at  the  left  in  42,  the  paper  may  be 
drawn  down  over  the  barrel  as  smoothly  as  a  glove.  An  additional 


38 


THE  STEAM  ENGINE   INDICATOR 


pinch  near  the  top,  and  a  squaring  of  corners  if  they  need  it,  will  render 
the  operation  complete. 

Another  method  is  to  put  the  paper  under  both  clips,  as  at  the  right 
in  Fig.  42.     This  prevents  the  ends  from  sticking  out,  and  keeps  the 


FIG.  42. 

paper   smooth.     It   is   sometimes   drawn   through   one   clip   only,  as   is 
shown  in  Fig.  43. 

Now  turn  on  the  steam  and  warm  up  the  instrument.  On  non- 
condensing  engines  it  is  well  to  turn  the  cock  so  that  the  steam  will  blow 
out  into  the  atmosphere  until  it  shows  blue  and  dry.  When  the  water 


FIG.  43. 

has  disappeared  and  the  pencil  is  vibrating  smoothly,  the  paper-drum 
being  in  motion,  hold  the  pencil  lightly  against  the  paper  and  allow 
it  to  trace  the  diagram.  For  ordinary  purposes  of  exhibition,  showing 
the  valve  action,  distribution,  etc.,  one  revolution  is  sufficient  to  hold 
the  pencil  on.  To  show  the  governor  action,  variation  of  load,  etc.,  the 


APPLICATION  39 

pencil  will  have  to  be  held  on  for  a  number  of  revolutions;  and  when 
measuring  power,  the  pencil  should  be  allowed  to  pass  from  ten  to 
twenty  times  over,  and  the/average  diagram  measured.  Turn  the  cock 
off  and  bring  the  pencil  again  to  the  paper,  tracing  the  atmospheric 
line.  It  is  not  good  practice  to  trace  the  atmospheric  line  first,  as  the 
indicator  and  spring  are  not  then  heated  and  under  the  same  conditions 
as  when  the  diagram  is  taken. 

When  through  indicating,  remove  the  spring,  piston,  etc.,  from  the 
indicator,  and  allow  the  steam  to  blow  through  the  cylinder  once  or  twice, 
t'nscrew  the  spring  from  the  piston  and  cap,  dry  it  thoroughly,  and 
wipe  it  clean  with  a  greasy  cloth.  The  springs  are  the  vital  part  of  the 
instrument.  Upon  their  integrity  and  accuracy  the  value  of  all  your 
work  depends.  Too  much  pains  cannot  be  taken  to  have  them  per- 
fectly accurate  when  bought,  to  keep  them  from  deteriorating  by  rust 
or  otherwise,  and  to  ascertain  their  condition  from  time  to  time.  Wipe 
up  and  clean  the  levers,  oiling  the  joints,  and  you  will  find  the  instru- 
ment all  ready  for  application  next  time.  When  the  lighter  parts  have 
been  attended  to,  the  main  body  of  the  indicator  will  be  found  to  be 
quite  dry,  from  having  had  the  steam  blown  through  it,  and  may  be  cleaned 
like  the  rest  and  put  together. 


CHAPTER    IV 
THE  DIAGRAM 

WE  have  learned  how  to  correctly  set  up  a  motion,  apply  the  in- 
dicator, and  obtain  a  diagram.  It  now  remains  to  consider  what  this 
diagram  is,  and  what  can  be  determined  from  it. 

When  the  mathematician  or  statistician  desires  to  record  the  results 
of  a  series  of  observations  or  experiments  in  such  a  manner  that  they 
may  be  at  once  apparent  and  easily  comprehended,  he  has  recourse 
to  what  is  known  as  the  graphic  method.  Suppose,  for  instance,  it 


I  86 


\ 


180 


1  75 


Time  10     .16      .30      .45 

A.M. 


11       .15        .30       .45        12       .16       .30       .45 
M. 

FIG.  44. 


1        .16       30      .45 
RJL 


was  desired  to  represent  in  this  way  the  result  of  a  series  of  observa- 
tions of  the  temperature  of  feed-water  during  a  test.  Taking  a  piece 
of  paper  ruled  in  squares,  as  represented  in  Fig.  44,  and  which  is  known 
as  ordinate  paper,  set  off  the  time  upon  one  of  the  horizontal  lines,  as 
shown  at  the  bottom  of  the  figure,  allowing  two  spaces  for  each  fifteen 
minutes.  Allow  each  of  the  vertical  divisions  to  represent  one  degree 
of  temperature,  making  the  lines  so  figured  correspond  to  175,  180,  and 
185°.  At  10  o'clock  the  observation  showed  176°,  so  upon  the  line 
representing  that  time,  and  at  a  height  representing  176,  make  a  dot. 
Fifteen  minutes  later  the  temperature  had  gone  up  to  178°,  and  upon 
the  line  representing  10.15  and  at  a  height  representing  178  another  dot 
is  made.  Continuing  in  this  way  to  represent  the  results  of  each 

40 


THE  DIAGRAM 


41 


observation,  and  connecting  the  dots  by  lines,  we  obtain  a  diagram 
showing  at  a  glance  how  nearly  regular  the  pressure  was  maintained 
through  the  test,  to  what  extent  it  varied,  and  at  what  time  variations 
occurred. 

Let  us  apply  this  method  to  the  variations  of  pressure  in  the  cylinder 
of  a  steam  engine.  Suppose  we  have  an  engine  with  a  stroke  of  32  inches, 
working  with  steam  of  60  pounds  gage  pressure  and  a  vacuum  of  12 
pounds,  cutting  off  at  8  inches,  with  the  exhaust  valve  opening  for  re- 
lease when  the  piston  is  2  inches  from  the  end  of  the  stroke  and  closing 
for  compression  when  the  return  stroke  is  within  5  inches  of  completion. 


I     ! 

60-Lbs 


Foil. 


of  Cut  oft 


Steam  Lint- 


46-Lbs 


Sea  e     h 


30-Lbs 


15-Lbs 


^il  t-r 


c  Line 


1-Ali 


FIG.  45. 


Upon  a  sheet  of  paper  ruled  as  in  Fig.  45  draw  the  line  OX,  32  spaces 
long,  which  will  represent  the  32  inches  of  the  stroke,  so  that  we  can 
represent  the  successive  positions  of  the  piston  or  volumes  by  propor- 
tional distances  from  0  upon  this  line.  We  will  also  consider  each  of 
the  spaces  in  a  vertical  direction  to  represent  3  pounds  pressure,  and 
starting  with  OX  as  the  zero  line  can  lay  off  to  this  scale  the  pressures 
corresponding  to  the  different  positions  of  the  pistons,  the  point  0  being 
the  zero  point  of  both  volumes  and  pressures. 

In  the  first  place  since  the  pressure  of  the  atmosphere  is  15  pounds, 
approximately,  above  the  absolute  zero  of  pressure;  we  will  lay  off 


42  THE  STEAM  ENGINE  INDICATOR 

the  line  A  A,  five  spaces  above  the  zero  line,  to  represent  that  pres- 
sure; and  as  gage  pressures  are  reckoned  from  the  pressure  of  the  atmos- 
phere as  zero,  we  will  lay  off  above  the  atmospheric  line  20  spaces  to 
indicate  the  60  pounds  of  steam  with  which  the  engine  is  supplied;  and 
as  steam  is  allowed  to  enter  freely  for  one-quarter  of  the  stroke,  we  will 
draw  the  " steam  line"  at  this  height  and  8  of  the  horizontal  spaces 
in  length.  At  this  point  the  supply  is  cut  off,  and  the  volume  of  steam 
inclosed  allowed  to  expand,  the  pressure  decreasing  practically  in  an 
inverse  ratio  to  the  volume;  so  that  when  the  piston  has  arrived  at -the 
vertical  line  16,  and  the  volume  has  been  doubled,  the  pressure  will 
be  halved;  at  the  line  24,  where  the  volume  is  3  times  that  at  the  point 
of  cut-off,  the  pressure  will  be  one-third,  etc.,  and  we  can  calculate  the 
pressure  for  each  ordinate,  as  the  vertical  lines  are  called,  and  lay  out 
the  curved  expansion  line,  as  will  be  more  fully  explained  when  we 
come  to  consider  that  line  particularly.  At  a  point  in  this  line  two 
inches  from  the  end  of  the  stroke  the  exhaust  valve  opens,  locating  the 
point  of  release,  and  the  pressure  falls  away  to  that  of  the  condenser, 
12  pounds  below  the  atmospheric  pressure,  and  3  pounds  above  the 
zero  line.  Five  spaces  from  the  end.  of  the  return  stroke  we  locate 
the  point  of  compression,  where  the  exhaust  valve  closes,  and  the  steam 
remaining  in  the  cylinder  is  compressed,  as  shown  by  the  compression 
line,  until  steam  is  again  admitted  and  another  stroke  commenced. 

From  the  diagram  thus  laid  out  the  actual  action  of  the  steam  in 
the  cylinder  will  vary  from  many  causes;  and  an  actual  diagram  taken 
from  the  cylinder  with  a  steam  engine  indicator  in  which  the  vertical 
distances  are  determined  by  the  pressure  of  the  steam  against  a  spring 
of  known  tension  and  the  horizontal  distances  by  a  movement  derived 
from  and  proportional  to  that  of  the  piston  itself,  will  enable  us,  if 
correctly  taken,  to  determine  the  actual  pressure  in  the  cylinder  at 
each  point  of  the  stroke,  and  to  compare  these  pressures,  and  the  lines 
which  they  generate  in  connection  with  the  changing  volumes,  with 
the  theoretical  diagram  constructed  as  above.  We  are  thus  enabled 
to  see  how  much  of  the  available  pressure  is  realized  in  the  cylinder, 
With  what  degree  of  promptness  it  is  admitted,  and  how  well  the  pressure 
is  maintained  behind  the  moving  piston;  to  observe  how  the  valve 
performs  its  functions,  how  much  of  the  vacuum  is  realized  in  the 
cylinder,  or  with  what  facility  the  spent  steam  is  gotten  rid  of.  We 
have  also  the  data  for  calculating  the  average  unbalanced  pressure 
against  the  piston,  and  thus  of  determining  the  work  performed.  In  fact, 
a  properly  taken  diagram,  with  all  data  concerning  it,  is  full  of  interest 
and  instruction,  and  its  study  can  be  profitably  carried  to  great  refine- 
ment. In  succeeding  chapters  we  shall  consider  the  separate  lines  of 
the  diagram  successively,  show  the  correct  form  and  common  depart- 


THE   DIAGRAM  43 

ures  tnerefrom,  with  their  causes,  and  lead  up  to  calculations  from  the 
diagram,  of  the  power  developed,  steam  consumption,  etc. 

RECAPITULATION — MOVEMENT    OF   THE    PISTON    AND   THE    ACTION    OF 
STEAM  IN  THE  CYLINDER. 

We  give  below  a  tabulated  summary  of  the  entire  diagram  showing 
the  formation  of  the  various  lines  composing  it.  "  Reference  will  be  had 
to  Fig.  45. 

Admission  Line. — During  the  formation  of  this  line,  steam  is  admitted 
into  the  clearance  space,  raising  the  pressure  from  that  of  compression 
to  the  steam  chest  pressure. 

Steam  Line. — The  piston  is  moving  ahead  and  steam  is  being  admitted 
behind  it. 

Expansion  Line. — At  the  point  of  cut-off,  the  steam  port  closes  and 
the  steam  behind  the  piston  expands  into  a  gradually  increasing  volume 
and  with  a  gradually  falling  pressure. 

Release  Line. — At  the  point  of  release  the  exhaust  port  opens, 
releasing  the  pressure.  The  steam  rushes  into  the  exhaust  chamber, 
the  pressure  falling  rapidly  meanwhile. 

Exhaust  Line. — By  the  time  the  piston  has  started  on  its  return 
stroke,  the  pressure  has  reached  its  minimum  and  the  piston  makes  its 
return  stroke,  pushing  out  before  it  through  the  exhaust  port  the  steam 
which  has  just  been  used  in  propelling  it  through  its  forward  stroke 
from  0  to  32. 

Compression  Line. — At  the  point  of  compression  the  exhaust  port 
closes,  confining  in  the  cylinder  a  small  quantity  of  steam  at  a  low 
pressure.  This  steam  fills  the  clearance  space  and  the  end  of  the 
cylinder  up  to  the  face  of  the  piston.  As  the  piston  completes  its 
return  stroke,  this  confined  steam  is  compressed  into  a  continually 
decreasing  space,  its  pressure  rising  meanwhile,  until  at  the  lower  end 
of  the  admission  line  of  the  steam  port  again  opens,  admitting  live  steam 
which  runs  the  pressure  up  to  that  of  the  steam  line. 


CHAPTER   V 
THE   ADMISSION   LINE 

THE  admission  line  shows  the  manner  in  which  steam  is  admitted 
to  the  cylinder.  Under  normal  conditions  admission  takes  place 
suddenly  while  the  piston  is  practically  standing  still  at  the  end  of 
the  stroke,  resulting  in  a  straight  line  perpendicular  to  the  atmospheric 
line,  into  which  the  compression  line  merges,  as  shown  at  A,  Fig.  46. 

In  order  that  the  admission  line  may  be  thus  erect,  it  is  necessary 
that  the  steam  valve  shall  be  open  so  as  to  admit  the  full  pressure  before 
the  piston  commences  to  move  away;  and  this  involves  the  question  of 
lead,  or  the  amount  of  opening  which  the  valve  has  when  the  engine 
is  on  the  center,  and  which,  for  many  reasons,  it  is  desirable  to  keep 
as  small  as  possible  and  yet  allow  the  admission  line  to  be  perpendicular. 
As  the  steam  valve  is  allowed  to  become  late  in  opening,  and  the  piston 
gets  into  motion  before  the  steam  is  admitted,  the  admission  line  com- 
mences to  curve  inward,  as  at  B  and  (7,  the  leaning  tendency  increasing 
as  the  line  progresses  and  the  motion  of  the  piston  becomes  faster.  At 
D  is  shown  a  peculiar  admission  line  on  a  diagram  taken  by  the  author 
from  a  slide-valve  engine,  the  eccentric  of  which  had  slipped  so  as  to 
make  the  whole  valve  motion  late.  The  exhaust  closure  being  late  as 
well  as  the  steam  opening,  the  compression  was  entirely  cut  out,  and  the 
back-pressure  line  b  continued  straight  up  the  end  of  the  stroke.  When 
the  piston  commenced  its  return  stroke  the  steam  valve  had  not  opened. 
The  exhaust-valve  had  by  that  time  closed,  the  space  between  the 
cylinder  head  and  the  retreating  piston  was  entirely  shut  in,  and  as  the 
piston  moved  away  a  vacuum  was  created,  running  the  pressure  down 
toward  a,  as  is  shown  by  the  arrow.  At  a  the  steam  was  admitted  and 
the  admission  line  ran  up,  leaving  the  loop  on  the  heel  of  the  diagram, 
as  shown. 

The  admission  line  may  lean  in,  however,  from  another  cause  than 
that  of  the  steam-valves  being  late,  as  the  author  found  in  procuring 
the  diagram  whose  admission  line  is  reproduced  at  E.  The  natural 
inference  from  the  appearance  of  the  diagram  would  be  that  the  engine 
was  late  all  around,  but  the  fact  is  that  the  steam-valve  has  plenty  of 
lead  and  opens  before  the  return  stroke  is  completed;  but  the  exhaust- 
valve  is  so  late  that  it  not  only  does  not  close  for  compression,  but  does 

44 


THE   ADMISSION   LINE 


45 


not  close  until  the  piston  has  got  well  started  on  the  forward  stroke, 
so  that  the  steam  is  blowing  right  through  into  the  exhaust  and  cannot 
keep  the  pressure  up.  As  the  exhaust  closes,  however,  the  pressure  is 
increased,  but  the  piston  is  moving  away  so  rapidly  that  the  line  never 
becomes-erect. 

The  amount  of  compression  has  a  great  deal  to  do  with  the  appear- 
ance of  the  admission  line.  The  effect  shown  at  F  is  a  very  common 
one,  produced  by  the  pressure  running  up  by  compression  to  the  point 


ir 


FIG.  46. 


and  falling  away  on  account  of  late  admission  as  the  piston  starts  back 
before  the  steam-valve  opens,  forming  the  loop.  A  more  aggravated 
case  of  the  same  action  is  shown  at  G,  which  represents  the  condition  in 
which  an  old-fashioned,  upright  Corliss  engine  ran  for  a  number  of 
years.  This  loop  assumes  all  sorts  ef  forms,  according  to  the  relations 
of  the  compression  and  admission,  and  the  proportions  of  the  openings 
and  the  piston  speed;  and  may  even  be  formed  when  the  steam-valve 
opens  promptly,  by  excessive  compression,  as  frequently  seen  on  diagrams 
from  the  ordinary  type  of  single  valve,  high-speed  engines  with  shaft 
governors,  where  the  compression  is  increased  as  the  load  diminishes, 
resulting  in  admission  lines  like  those  shown  at  H  and  L  In  the  first 


46  THE   STEAM   ENGINE   INDICATOR 

of  these  the  pressure  is  so  low  that  the  compression  line  extends  above 
it,  and  when  the  steam-valve  opens,  there  is  an  escape  of  steam  from 
the  cylinder  and  the  pressure  is  lowered  to  that  at  which  the  steam  will 
flow  from  the  chest.  The  appearance  at  /  is  produced  when  the  engine 
is  lightly  loaded,  so  that  the  compression  is  very  considerable. 

A  sharp  point  at  the  top  of  the  admission  line  is  usually  an  indica- 
tion of  too  much  lead,  and  it  will  be  found  to  result  in  smoother  running 
if  the  corner  is  just  given  an  indication  of  rounding,  as  at  A.  The  pro- 
jection is  due  to  the  fling  of  the  moving  parts  carrying  the  pencil  above 
the  point  due  to  the  pressure. 

Just  as  a  tardy  action  of  the  steam-valve  results  in  producing  an  in- 
ward leaning  of  the  admission  line,  so  a  too  early  opening  of  that  valve 
will  result  in  the  production  of  a  line  which  leans  outward,  as  shown 
at  K.  This  is  to  be  avoided,  as  it  puts  an  injurious  strain  on  all  the  work- 
ing parts  of  the  engine,  pushing  with  all  the  force  of  the  steam  pressure 
per  square  inch  multiplied  by  the  piston  area  upon  the  crank  as  it  is  com- 
ing up  over  the  center,  and  crowding  the  shaft  hard  into  the  main  bear- 
ing to  no  purpose.  It  simply  sets  the  steam  pressure  to  work  against 
the  desired  movement  of  the  engine,  and  robs  the  diagram  of  the  effective 
area  between  the  admission  line  and  the  perpendicular  dotted  line  K, 
which  indicates  the  position  the  admission  line  should  really  occupy. 
Any  engine  which  is  in  line  and  properly  adjusted  in  the  connections 
should  run  at  the  speed  for  which  it  is  designed  better  with  enough  lead 
to  bring  the  admission  line  upright,  than  it  does  with  more,  and  if  the 
upright  is  to  be  departed  from  at  all,  it  had  better  be  in  the  direction 
of  making  the  valve  late  than  in  that  of  giving  the  engine  steam  before 
it  is  ready  for  it. 


CHAPTER   VI 
THE  STEAM  LINE 

FROM  the  steam  line  of  the  indicator  diagram  may  be  determined 
what  percentage  of  the  boiler  pressure  is  realized  in  the  cylinder  and 
how  well  this  pressure  is  maintained  up  to  the  point  of  cut-off.  Steam 
or  any  other  fluid  will  not  flow  without  a  difference  of  pressure  between 
the  vessel  from  which  it  flows  and  that  into  which  it  is  delivered,  and 
this  difference  in  pressure  must  be  sufficient  to  overcome  the  frictional 
resistance  of  the  connecting  pipes  and  passages.  It  is  absolutely  im- 
possible, therefore,  to  maintain  in  the  cylinder  the  same  pressure  that 
is  carried  in  the  boiler,  although  with  short  connections,  ample  passages, 
and  low  piston  speeds  a  very  large  percentage  can  be  realized. 

In  a  really  good  diagram  the  steam  line  will  appear  about  as  at  A,  Fig. 
47,  approaching,  in  its  height  above  the  atmospheric  line,  the  distance 
indicated  by  the  boiler  pressure  laid  off  to  the  same  scale  as  that  of  the 
spring  with  which  the  diagram  is  taken,  as  shown  by  the  dotted  line, 
and  remaining  horizontal,  or  very  nearly  so,  up  to  the  point  of  cut-off. 
When  the  connecting  pipe  and  passages  are  small  for  the  piston  speed 
and  diameter,  the  linear  velocity  of  the  flow  becomes  so  great  that  a 
greater  difference  in  pressure  is  necessary  to  overcome  the  increased 
resistance,  and  the  steam  line  falls  away,  as  at  B,  sufficiently  to  keep 
up  the  difference  necessary  for  such  a  rate  of  flow,  as  at  a  and  b,  the 
difference  at  a  being  sufficient  to  maintain  the  lesser  velocity  at  the  begin- 
ning of  the  stroke,  while  the  greater  difference  in  pressure  at  6  is  necessary 
when  the  piston  has  gained  the  greater  speed  due  to  that  position  in  the 
stroke. 

Such  a  falling  away  may  be  due  either  to  faulty  design  or  setting 
of  the  ports  and  valve  of  the  engine  itself,  in  which  case  the  loss  of 
pressure  will  occur  chiefly  between  the  steam  chest  and  the  cylinder; 
or  to  a  long,  tortuous,  or  insufficient  connection  between  the  engine 
and  boiler,  in  which  case  the  loss  of  pressure  would  occur  between  the 
boiler  and  the  steam  chest.*  To  which  of  these  causes  the  loss  is  mainly 
due,  and  how  much  of  it  is  due  to  each,  may  be  determined  by  applying 
the  indicator  to  the  steam  chest,  taking  the  motion  from  the  cross-head 
just  the  same  as  when  the  indicator  is  upon  the  cylinder.  Such  a  diagram 

*  See  Chapter  XIII  on  Errors  of  the  Diagram. 

47 


48 


THE   STEAM   ENGINE   INDICATOR 


should  be  taken  by  transferring  the  indicator  from  the  cylinder  to  the 
steam  chest  without  disturbing  the  paper  on  which  the  cylinder  diagram 
has  been  taken,  and  maintaining  the  boiler  pressure,  load  and  speed 
constant,  in  order  to  best  show  the  relations  of  the  diagrams.  A  still 
better  way,  when  plenty  of  indicators  are  available,  is  to  have  an  instru- 
ment on  both  the  chest  and  cylinder,  take  simultaneous  diagrams,  to 
the  same  scale,  and  transfer  them  to  one  card,  by  making  the  atmos- 


\ 


V 


FIG.  47. 


pheric  lines  identical.  This  may  be  handily  done  by  cutting  the  card 
from  the  cylinder  close  to  the  steam  line  at  the  top,  and  reducing  its 
length  so  as  only  to  include  the  diagram.  Then  extend  the  atmospheric 
line  to  the  ends  of  the  card,  extend  the  atmospheric  line  on  the  steam 
chest  card,  and  place  the  two  cards  so  that  the  atmospheric  lines  will 
coincide  as  i'n  Fig.  48,  one  diagram  being  directly  beneath  the  other. 
Being  made  from  the  same  reducing  motion,  their  lengths  should  be 
the  same. 

The  diagram  shown  above  the  ordinary  cylinder  diagram  in  Fig. 
48  is  a  conventional  steam  chest  diagram.  At  a  the  valve  opens  to  let 
steam  into  the  cylinder,  and  the  outrush  of  steam  reduces  the  steam 


THE   STEAM   LINE 


49 


pressure  in  the  chest  until  there  is  the  difference  between  the  boiler 
pressure  and  the  pressure  in  the  chest  indicated  by  the  space  be,  between 
the  line  of  boiler  pressure  (which  should  be  drawn  in  on  the  diagram  at 
a  height  measured  from  the  atmospheric  line  by  the  same  scale  with 
which  the  diagrams  were  taken)  and  the  lower  line  of  the  chest  diagram. 
Understand,  the  vertical  distance  between  the  line  of  boiler  pressure 
and  the  lower  line  of  the  chest  diagram  represents  the  loss  of  pressure 
between  the  boiler  and  the  steam  chest  at  that  point.  The  space  between 
the  lower  line  of  the  steam  chest  diagram  and  the  steam  line  of  the  cylinder 
diagram  at  any  point  in  the  stroke  is  a  measure  of  the  loss  of  pressure 
between  the  steam  chest  and  the  cylinder.  The  greater  the  distance  from 
the  boiler,  the  smaller  the  pipe,  and  the  greater  the  number  of  turns, 
the  greater  the  loss  of  pressure  between  the  steam  chest  and  the  boiler, 


Boiler  Pressure 


FIG.  48. 

and  the  greater  the  area  of  the  steam  chest  diagram.  The  smaller, 
longer,  and  more  crooked  the  ports,  the  greater  the  reduction  between 
the  steam  chest  and  cylinder  and  the  greater  the  lost  area  between  the 
diagrams.  Following  out  the  outline  of  the  steam  chest  diagram,  the 
pressure  continues  to  fall  along  the  line  acd  as  the  piston  moves  faster 
and  faster  until  the  cut-off  valve  closes  and  the  draft  of  steam  from  the 
chest  ceases,  when  the  pressure  in  the  chest  commences  to  recover  and 
runs  well  or  quite  up  to  boiler  pressure  as  the  flow  of  steam  is  stopped. 
It  may  even  run  above  the  boiler  pressure  on  account  of  the  momentum 
of  the  moving  column  of  steam  in  the  connecting  pipes.  A  similar 
action  upon  the  other  end  completes  the  diagram.  It  will  be  seen 
that  in  this  way  the  cause  of  any  excessive  loss  of  pressure  can  be 
located  exactly  and  the  relative  importance  of  changes  in  the  engine 
or  piping  determined. 


50  THE  STEAM   ENGINE   INDICATOR 

The"  fall  of  pressure  in  the  steam  chest,  and  thus  the  shape  of  the 
steam  line,  may  be  considerably  affected  by  the  amount  of  compres- 
sion used.  Suppose  an  engine  to  cut  off  at  quarter  stroke  and  to  have 
5  per  cent  clearance.  The  total  displacement  up  to  cut-off  is  25  +  5=30 
per  cent  of  the  whole  displacement.  This  is  the  volume  which  must 
be  filled  from  the  boiler,  and  the  clearance  is  ^  or  ^  of  it.  But  even 
a  good  engine  uses  20  per  cent  more  steam  than  would  be  accounted 
for  by  filling  this  volume  the  given  number  of  times  an  hour.  This 
steam  is  condensed  upon  the  containing  surfaces  which  have  just  been 
exposed  to  the  exhaust  pressure  and  refrigerated  by  the  evaporation 
from  them  of  the  water  which,  in  a  vacuum,  evaporates  at  very  low 
temperatures  and  even  in  a  non-condensing  engine  at  a  temperature 
below  that  of  the  metal.  Suppose  that  another  sixth  is  thus  disposed 
of  and  you  have  one-third  of  the  total  steam  which  the  engine  requires 
to  be  furnished  from  the  steam  chest  before  the  piston  moves  off  from 
the  center.  If  the  clearance  is  empty  when  the  admission  valve  opens, 
this  draft  will  make  a  serious  reduction  in  the  steam  chest  pressure 
and  will  reduce  the  height  of  the  steam  line.  If  the  clearance 
has  been  largely  filled  by  compression  the  draft  will  be  correspond- 
ingly less  and  the  steam  line  will  be  higher,  especially  at  its  com- 
mencement. This  is  the  reason  why  compression  often  makes  a  steam 
line  fall  away,  not  by  lowering  its  final  but  by  raising  its  initial 
-  pressure. 

In  order  to  prevent  an  undue  fall  of  pressure,  and  wire  drawing  of 
the  steam,  the  passages  leading  to  the  cylinder  should  be  so  propor- 
tioned that  at  no  point  the  linear  velocity  of  flow  shall  exceed  6000  feet 
per  minute.  This  can  be  done  by  making  the  passages  bear  the  same 
proportion  to  the  cross-sectional  area  of  the  cylinder  that  the  piston 
speed  does  to  6000;  i.e.,  take  for  the  smallest  cross-sectional  area  of 
the  steam  pipe  or  passages  such  as  fraction  of  the  cross-sectional  area 
of  the  cylinder  as  is  indicated  by  writing  the  piston  speed  in  feet  per 
minute  as  a  numerator  over  6000  as  a  denominator. 

For  a  piston  speed  of  600  feet  per  minute,  for  instance,  the  smallest 
cross-section  of  the  pipe  or  port  should  not  have  an  area  less  than  -£££vt 
or  one-tenth  of  the  cross-sectional  area  of  the  cylinder. 

On  engines  with  large  steam  chest  capacity  the  appearance  at  C, 
Fig.  47,  is  often  met,  the  large  volume  of  steam  already  at  hand  sufficing 
to  keep  the  pressure  up  at  the  commencement  of  the  stroke,  but  when 
the  piston  movement  becomes  more  rapid  and  the  draft  from  the  boiler 
begins  in  earnest,  a  greater  difference  in  pressure  is  required  to  maintain 
the  flow,  and  the  line  drops  away,  as  shown. 

If  there  is  any  tendency  to  fall  away  on  the  part  of  the  steam  line, 
it  will,  under  equal  conditions,  manifest  itself  most  decidedly  on  the 


THE  STEAM   LINE 


51 


head  end  of  the  cylinder,  as  the  piston  movement  is  faster  on  that  end, 
owing  to  the  angularity  of  the.  connecting-rod. 

The  downward  tendency  of  the  steam  line  increases  with  its  length, 
for,  as  the  stroke  progresses,  the  velocity  of  the  piston  movement  becomes 
greater  up  to  midstroke  and  the  rate  of  flow  accelerated.  It  is  there- 
fore very  rarely  that  we  find  a  long  steam  line  on  a  cut-off  engine,  which 


FIG.  49. 

does  not  commence  to  fall  away  seriously  from  the  initial  pressure,  al- 
though it  may  hold  up  nicely  during  the  earlier  portion  of  the  stroke. 
A  decided  example  of  this  action  is  seen  in  diagrams  from  cut-off 
engines  when  cut-off  does  not  take  place.  Such  a  diagram  is  shown 
at  E,  Fig.  47,  and  it  will  be  seen  that  although  the  steam  line  is  well 
maintained  at  the  commencement  of  the  stroke,  the  steam  follows  the 


FIG.  50. 

piston  with  more  difficulty  during  the  rapid  movement  in  the  middle 
of  the  cylinder  and  the  pressure  falls  away,  recovering  somewhat  as  the 
movement  grows  slower  on  approaching  the  other  end.  The  same  effect 
is  observable  at  times  upon  diagrams  from  throttle-governed  engines; 
but  as  the  steam  lines  of  such  diagrams  depend  upon  the  vagaries  of  a 
governor  situated  between  the  cylinder  and  the  source  of  steam  supply, 
little  interest  attaches  to  their  study  as  denoting  the  action  of  the  steam. 
In  throttle-governed  engines  the  area  of  the  diagram,  which  is  the 
measure  of  the  amount  of  work  performed,  is  varied  in  accordance  with 


52  THE   STEAM   ENGINE   INDICATOR 

the  demands  of  the  load  by  increasing  the  vertical  distance  between  the 
steam  line  and  the  line  of  counter  pressure,  as  from  a  to  b  (Fig.  49)  for 
a  light  load  and  form  a  to  c  for  a  heavy  load,  while  in  the  automatic 
cut-off  engine  the  same  object  is  effected  by  varying  the  length  of  the 
steam  line  by  cutting  off  the  steam  earlier  or  later  in  the  stroke,  as 
from  a  to  b  (Fig.  50)  for  a  light  load  and  from  a  to  c  for  a  heavy  load. 

Diagrams  are  sometimes  met  with  which  have  no  steam  line,  the 
load  being  so  light  that  the  expansion  of  the  steam  in  the  clearance  is 
sufficient  to  keep  the  engine  in  motion.  In  this  case  the  expansion 
line  meets  the  admission  line  at  a  point,  as  at  D,  Fig.  47. 

The  shape  of  the  steam  line  is  often  modified  by  the  admission,  and 
it  will  be  realized  from  the  remarks  about  the  admission  line  in  the  last 
chapter  that  it  is  difficult  to  say  when  the  one  leaves  off  and  the  other 
begins,  under  frequently  occurring  conditions. 


CHAPTER  VII 
THE  EXPANSION  LINE 


IN  all  engines  in  which  any  pretension  ig  made  to  economy,  steam 
is  used  expansively,  the  supply  being  cut  off  at  some  point  in  the  stroke, 
determined  either  automatically  by  the  governor  or  positively  by  the 
valve.  By  this  means  the  piston  is  urged  not  only  while  there  is  a  direct 
draft  of  steam  from  the  boiler,  but  by  the  expansive  force  of  the  steam 
in  the  cylinder  after  this  draft  has  ceased. 

Referring  to  Fig.  51,  let  OX  represent  the  stroke  of  an  engine,  and 
OA  the  pressure  of  steam  in  the  cylinder  at  the  commencement  of  the 
stroke;  then,  since  the  energy  is 

^  A  r>  n 

the  pressure  multiplied  by  the 
space  through  which  it  is  exerted, 
we  should  have  for  the  energy 
developed  in  a  cylinder  in  which 
the  initial  pressure  is  continued 
to  the  end  of  the  stroke  a  value 
proportional  to  the  area  of  the 
rectangle  ABXO,  and  the  cylin- 
der would  require  to  be  com-  6" 
pletely  filled  with  steam  from  the 
boiler  at  each  stroke.  If  instead 

of  allowing  the  steam  to  follow  full  stroke  the  supply  is  cut  off  at  mid- 
stroke,  as  indicated  at  C,  there  would  be  behind  the  piston  at  this  point  a 
half-cylinderful  of  steam  at  the  initial  pressure,  which,  as  the  piston  moves 
onward,  will  be  expanded,  allowing  its  pressure  to  fall  along  the  curved 
line  CD.  The  energy  generated  will  now  be  proportional  to  the  area 
ACDXO,  less  by  the  area  BCD  than  it  was  before;  but  the  amount  of 
steam  called  for  from  the  boiler  has  been  only  one-half  as  much  as  when 
the  engine  followed  full  stroke,  and  the  energy  represented  by  the  shaded 
area  CDXE  has  been  gained  at  no  expense  for  extra  steam. 

Steam  in  expanding  in  an  engine  cylinder  under  the  conditions  of 
ordinary  practice  varies  in  pressure  so  nearly  in  an  inverse  ratio  to  its 
volume  that  we  can  use  this  law  in  laying  out  the  approximate  path 
that  the  curve  CD,  Fig.  51,  will  take. 

Supposing  an  engine  with  a  48-inch  stroke  to  cut  off  at  8  inches  or 

53     • 


E 
FIG.  51. 


54 


THE   STEAM   ENGINE   INDICATOR 


one-sixth  of  the  stroke,  with  steam  of  an  absolute  pressure  of  90  pounds 
B  (about  75  pounds  by  the  gage).     Representing  the 

stroke  of  this  engine  by  the  base  line  of  the  diagram 
Fig.  52,  we  should  have,  when  the  piston  had  com- 
pleted the  eighth  inch  of  its  stroke,  one-sixth  of 
the  cylinder  full  of  steam  at  90  pounds  pressure, 
represented    by  the   area   OARS.     The  supply 
is  now  cut  off,  and  when  the  piston  has  arrived 
at  the  16-inch  point  the  steam  will  have  ex- 
panded to  double  its  volume  at  cut-off,  and 
its  pressure  will  be  reduced  to  one-half  or  45 
pounds,  represented  by  the  height  of  the 
point    C.     When   the   piston   had   pro- 
ceeded another   8    inches,  or    to    the 
24-inch    mark,   its    volume    would 
have  been  trebled  and  the  initial 
pressure  divided  by  three,  giving 


16 


24 
FIG.  52. 


48 


a  pressure  at  this  point  of  30  pounds,  represented  by  the  length  of  the 
line  24Z),  which  is  one-third  of  the  line  8J5,  representing  the  pressure  of 
the  initial  volume. 

In  the  same  way  we  would  find  one-fourth  the  pressure  when  the 
steam  had  been  expanded  to  four  times  the  initial  volume  at  E,  one- 
fifth  the  pressure  when  the  volume  had  attained  five  times  the  original 
at  F,  and  one-sixth  the  pressure  at  G,  where  the  volume  is  six  times 
what  it  was  at  the  point  of  cut-off.  In  this  way  the  pressures  at  various 
points  in  the  stroke  may  be  calculated  and  set  off  upon  ordinates 
representing  by  their  position  upon  the  horizontal  line  the  corresponding 
point  in  the  stroke,  and  a  curve  drawn  through  these  points  will  be  the 
theoretical  expansion  curve. 

As  a  simple  rule  for  finding  the  pressure  at  any  point  in  the  stroke : 
Multiply  the  absolute  pressure  at  the  point  of  cut-off  by  the  fraction  made 
by  writing  the  number  of  inches  of  the  stroke  completed  at  cut-off  as  a  numerator 
over  the  number  of  inches  completed  at  the  given  point  as  a  denominator. 


THE  EXPANSION  LINE  55 

For  example,  to  determine  the  pressures   at  C,  D,  E,  F,  G  in  the 
above  described  diagram  we  have: 

At  C  the  pressure  =  1^X90  =45  pounds 

•"  D 

"  E          " 

"  F 

11   G          " 


Notice  also  that  the  product  of  the  volume  and  pressure  is  constant. 
At  B  we  have  one  volume  and  90  pounds  and 


Volume.          Pressure. 

Product. 

At  B 

1 

X 

90 

=      90 

"   C 

2 

X 

45 

=      90 

"  D 

3 

X 

30 

=      90 

"  E 

4 

X 

22.5 

=      90 

it  p 

5 

X 

18 

=      90 

"  G 

6 

X 

15 

=      90 

The  pressure  for  any  volume  may  be  found  therefore  by  dividing  the 
initial  pressure  by  the  given  volume  in  terms  of  the  first  volume. 

This  is  a  case  of  inverted  proportion  and  may  be  readily  solved  by 
the  slide  rule  by  inverting  the  slide  and  setting  the  index  to  the  initial 
pressure.  In  Fig.  53  the  index  of  the  inverted  slide  is  set  at  120  on 
the  lower  scale.  Under  the  2  of  what  is  now  the  top  of  the  slide  read 
60  on  the  bottom  scale  for  two  volumes  under  the  3,  40  for  three  volumes, 
etc.  There  is  a  special  rule  called  the  Duplex  made  with  an  inverted 
scale,  shown  in  Fig.  54,  so  that  the  two  scales  in  use  are  contiguous  and 
the  number  right  side  up. 

In  applying  this  curve  to  an  indicator  diagram,  the  fact  must  be 
taken  into  account  that  besides  the  volume  of  steam  represented  by 
the  piston  displacement  up  to  the  point  of  cut-off  there  is  the  steam 
in  the  clearance  spaces,  which  will  share  in  the  expansion,  and  the  initial 
volume  must  be  made  to  include  this  steam.  We  will  apply  the  curve 
to  the  diagram  in  Fig.  55  by  one  of  the  simplest  methods.  This  diagram 
is  4  inches  in  length,  and  we  will  assume  a  clearance  of  2^  per  cent. 
Two  and  a  half  per  cent  of  4  inches  is  one-tenth  of  an  inch,  by  the 
addition  of  which  we  will  increase  the  length  of  the  diagram  at  the 
admission  end  by  drawing  in  the  clearance  line  AO  one-tenth  of  an 
inch  from  the  extreme  end  of  the  diagram.  Draw  the  line  of  absolute 
pressure  14.7  pounds  below  the  atmospheric  line.  With  ordinarily  high 
scales  15  pounds  is  sufficiently  accurate.  Now  at  the  point  of  cut-off 
C  there  will  be  in  the  cylinder  a  volume  of  steam  proportional  to  the 
area  AC  10  of  a  pressure  proportional  to  the  line  1C.  At  right  angles 
to  the  line  of  absolute  zero,  OX,  erect  perpendiculars  at  points  where 
it  is  desired  to  locate  the  curve.  As  the  curve  changes  more  rapidly 


* 

I 


CO 

__E|J5CT 


eico  - 


»  0 


THE   KXPAN<ln\    LINE 


57 


just  after  cut-off,  it  is  advisable  to  put  in  these  perpendiculars  more 
closely  in  the  earlier  portion  of  the  stroke,  as  shown,  and  this  is  especially 
true  of  diagrams  with  large  ratios  of  expansion,  i.e.,  early  points  of 
cut-off.  Xow  take  in  the  dividers  the  width  of  the  space  representing 
the  initial  volume,  i.e.,  the  length  of  the  line  AC  or  01,  and  from  the 
base  of  the  first  ordinate  a  measure  off  an  equal  distance  aa'  =AC, 
upon  the  zero  line.  A  line  connecting  the  point  of'  cut-off  C  with  a' 
will  cross  the  vertical  ordinate  a  at  the  point  through  which  the  curve 
must  pass.  From  the  base  of  the  second  ordinate  6  set  off  the  same 
distance  W  =A C,  and  a  line  joining  the  point  of  cut-off  and  b'  will  cut 
the  ordinate  6  at  the  point  through  which  the  curve  should  pass  at  that 
point  of  the  stroke.  Proceeding  in  this  manner  with  c  and  c',  d  and  d', 
and  as  many  other  ordinates  as  are  essential,  the 
points  through  which  the  curve  will  pass  may  be 
located  and  the  curve  traced  in  as  indicated  by 
the  dotted  line.  In  practice  it  is  not  necessary 
to  draw  the  lines  from  the  point  of  cut-off, 
but  simply  to  mark  the  point  at  which  the 
straight  edge  crosses  the  ordinate,  as 
shown  upon  the  ordinate  d.  By  spac- 
ing the  ordinates  abc,  etc.,  the  same 
distance  from  each  other  that 
the  point  of  cut-off  is  from 
the  clearance  line,  i.e.,  mak- 


ing  the  distance  between  the  ordinates  equal  to  AC  or  01,  the  base  of 
one  line  may  be  used  as  the  point  from  which  to  rule  to  the  point  of 
cut-off  to  locate  the  curve  on  the  preceding  ordinate,  but  this  method 
does  not,  with  ordinary  diagrams,  give  a  sufficient  number  of  ordinates 
to  locate  the  curve  accurately  in  the  earlier  portion  of  the  stroke. 

Another  method  frequently  used  for  laying  out  the  theoretical  curve 
is  shown  in  Fig.  56.  Allow  OX,  as  in  the  previous  examples,  to  represent 
the  line  of  absolute  zero,  the  line  AC,  by  its  distance  from  the  zero  line, 
the  initial  pressure,  and  by  its  length  the  volume  of  steam  up  to  the 


58 


THE   STEAM  ENGINE   INDICATOR 


point  of  cut-off,  including  that  in  the  clearance,  determined  as  pre- 
viously shown.  Erect  any  number  of  perpendicular  ordinates,  as  1, 
2,  3,  4,  5,  6,  7,  8,  at  points  where  it  is  desired  to  locate  the  position  of 
the  curve.  Continue  the  line  AC  for  the  full  length  of  the  diagram  AD. 
The  point  through  which  the  cruve  would  pass  on  any  ordinate,  as  6, 
for  example,  is  found  by  connecting  its  top  E,  as  determined  by  the  line 
AD,  with  the  point  0.  The  line  EO  will  cross  the  line  1C  at  the  point  e, 
which  indicates  the  height  at  which  the  curve  would  pass  on  the  line  6E1, 
and  may  be  transferred  to  that  line  by  drawing  the  horizontal  ee' '.  In 
the  same  way  the  point  /'  is  located  upon  the  ordinate  5F,  and  at  as 
many  other  positions  as  are  necessary  to  determine  the  course  of  the 
curve  with  the  necessary  accuracy. 


1234 


6 

FIG.  56. 


The  curve  which  we  have  been  describing,  and  which  corresponds 
with  a  constant  product  for  pressures  and  volumes,  is  a  rectangular 
hyperbola;  rectangular  because  the  asymptotes,  as  the  lines  OA  and 
OX  are  called,  are  at  right  angles.  Let  the  rectangle  OABl,  Fig.  57, 
represent  by  its  height  the  pressure  and  by  its  width  the  volume  of  an 
amount  of  steam.  The  area  of  a  rectangle  representing  this  amount 
of  steam  at  any  other  volume  (the  pressure  changing  accordingly)  will 
be  the  same  as  the  area  of  OABl,  for  the  area  is  the  product  of  height 
and  width,  which  represent  respectively  the  pressure  and  volume,  and 
with  hyperbolic  expansion  the  product  of  the  pressure  and  volume  is 


THE   EXPANSION  LINE 


59 


constant,  as  shown  on  page  55.  With  the  volume  doubled,  therefore, 
the  rectangle  representing  the  new  condition  would  be  OCD2,  one-half 
the  height  and  twice  the  width,  and  at  4  volumes  the  rectangle  becomes 
a  square,  the  lines  representing  the  pressure  and  volume  being  of  equal 
length.  After  this  point  the  lines  representing  volumes  become  longer 
than  those  representing  pressure,  but  we  shall  have  simply  a  repetition 
of  the  rectangles  for  the  earlier  volumes  with  their  length  horizontal 
instead  of  vertical.  The  rectangle  OGH8,  representing 
24o~~|B  8  volumes  and  2  units  of  pressure,  is  the  same  as  the  rect- 
angle OCD2,  representing  2  volumes  and  8  units  of  pressure. 
Thus  it  will  be  seen  that  the  curve  is  the  same  on  both  sides 
of  the  diagonal  OF,  which  is  called  the  axis,  and  that  the 
portion  of  the  curve  which  lies  between  F  and  J  is  precisely 
similar  to  that  which  lies  between  B  and  F. 

It  is  a  property  of  this  curve  that  a  line  drawn  across  so  as 
to  intersect  it  in  two  places,  as  KL,  mN,  WP,  will  cut  the 
\      |  \          curve  at  equal  distances  from  the  asymptotes  at  both  ends. 
It  is   easily  seen  that   the   point  D  on  the  curve   is  the 
same  distance  from  K  that  H  is  from  L.     As  the  top 
of  the  line   is   carried  downward  from  D  as  to  W,  the 
distance  is  decreased  as  to  WD,  but  the  curvature 
is  such  as  to  make  the  distance  QP  upon  the 
other  end   precisely  equal.      So    also    the    in- 
creased length  in  the  position  mD  is  met 
by  a  similar  increase   in   the  distance 
RN  at   the  other   end   of   the   line. 
.  This  is   true  whatever   point   is 


chosen    upon 
whatever 


the    curve 
inclination 


or 
is 


given   to    the   line,   so 


long  as  it  cuts  the  curve  in  two  places  and  both  asymptotes.     For  instance, 
on  the  line  ST  placed  at  random,  the  distances  SV  and  Tu  are  equal. 

This  property  is  made  use  of  in  several  constructions  used  upon 
indicator  diagrams,  one  of  which  is  laying  out  the  curve  as  shown  in  Fig. 
58.  Through  any  point  upon  the  expansion  line,  as  C,  draw  straight 
lines  to  the  line  bounding  the  clearance  in  one  direction  and  to  the  line 


60 


THE   STEAM   ENGINE   INDICATOR 


of  absolute  vacuum  in  the  other.  Upon  the  line  1  1'  set  off  a  distance 
from  1',  equal  to  1C.  Upon  the  line  2  2',  set  off  a  distance  from  2' 
equal  to  2C,  and  continue  the  process  upon  the  other  lines  as  shown. 
The  theoretical  curve  passes  through  the  points  just  found.  In  prac- 
tice it  is  unnecessary  to  draw  lines,  distances  being  laid  off  by  means 
of  the  dividers  against  the  edge  of  the  ruler.  This  principle  is  also  used 
to  determine  at  what  point  cut-off  should  occur,  assuming  initial  pres- 
sure to  be  uniformly  maintained,  in  order  that  the  expansion  line 
may  pass  through  point  A.  Drop  a  perpendicular  line  from  A, 
Fig.  59,  to  the  line  of  zero  pressure,  and  connect  the  point 
B  of  its  intersection  with  the  point  P  upon  the  line  of  zero 
volumes,  indicating  by  its  height  the  given  pressure.  A 
line  pb,  parallel  to  PB  and  passing  through  the  given 
point  A,  will  cut  the  line  PC  at  the  required  point  at 
which  expansion  should  commence  in  order  that  the 
curve  may  pass  through  A.  For  under  these,  con- 
ditions the  triangle  PpC  is  the  same  as  the  triangle 
A  Bb,  and  upon  the  line  bp  the  points  A  and  C  are 
equidistant  from  the  asymptotes.  The  point  of 
cut-off  for  any  other  initial  pressure  may  be 
determined  in  the  same  way  by  varying 
the  position  of  the  point  P,  as  indi- 
cated by  the  dotted  lines. 

Another  construction  some- 
times used   upon  the  ex- 
pansion line  of  an  indi- 
cator    diagram     is 


FIG.  58. 

shown  in  Fig.  60.  This  is  for  the  purpose  of  finding  the  position 
of  the  line  OA,  bounding  the  clearance  space.  From  any  two  points, 
as  BC,  upon  the  established  portion  of  the  curve  draw  lines  as 
BD  and  CE,  parallel  to  the  atmospheric  line,  also  the  perpendicu- 
lar lines  BE  and  CD,  forming  a  rectangle.  At  a  distance  below 
the  atmospheric  line  corresponding  to  14.7  pounds  on  the  scale  of 
the  diagram  draw  the  line  of  absolute  zero  of  pressure  OX.  The 
diagonal  DE  of  the  rectangle  BDCE  will,  if  continued,  cut  the  line  of 


THE  EXPANSION   LINE 


61 


zero  pressure  at  the  point  0  of  zero  volume,  from  which  point  the  per- 
pendicular line  OA ,  the  position  of  which  we  are  seeking,  may  be  erected. 


FIG.  59. 

The  theoretical  curve  is  of  value  in  showing  what,  under  given  condi- 
tions of  pressure  and  expansion,  a  diagram  may  be  expected  to  be, 
and  serving  as  a  basis  of  comparison  for  the 
actual  diagram.  It  is  not  precise,  however, 
and  too  much  stress  should  not  be  placed 
upon  itS  indications  unless  very  marked. 
The  law  that  the  product  of  the  vol- 
ume and  pressure  remains  contant 
is  true  only  of  a  perfect  gas,  and 
of  this  only  when  its  tempera- 
ture remains  constant.  The 
temperature  of  steam  falls 
as  it  is  expanded  and 


/O 


FIG.  60. 


62 


THE   STEAM   ENGINE   INDICATOR 


the  volume  would  be  expected  to  contract  by  such  cooling  so  as 
to  bring  the  expansion  curve  below  that  drawn  upon  the  pv=  constant 
assumption.  And  it  would  so  fall  if  a  constant  quantity  of  steam  were 
being  dealt  with.  But  steam  is  being  generated  in  the  cylinder  through- 
out the  expansion.  As  explained  above  considerable  of  the  steam 


FIG.  61. 

admitted  to  the  cylinder  is  condensed  and  is  present  as  hot  water.  When 
the  pressure  has  fallen  by  expansion  so  that  the  water  is  above  the  boiling- 
point  at  the  new  pressure  the  water  commences  to  pass  into  steam,  taking 
from  the  cylinder  surfaces  and  the  other  water  the  latent  heat  needed 
for  its  evaporation,  and  the  additional  steam  thus  made  is,  with  ordinary 


FIG.  62. 

un jacketed  engines  and  steam  which  is  not  superheated,  just  about  enough 
to  keep  the  expansion  line  up  to  that  laid  out  according  to  this  law. 
Any  serious  departure  from  the  curve  thus  laid  out  indicates  something 
which  should  be  looked  after.  The  line  drawn  by  the  indicator  is  likely 
to  run  below  the  plotted  curve  at  the  commencement  and  above  it  at 


THE   EXPANSION  LINE  63 

the  end,  as  re-evaporation  becomes  more  vigorous.  The  curve  and  law 
are  also  of  use  in  designing,  and  in  computing  probable  mean  effective 
pressures,  as  will  be  shown  later.  If  the  actual  curve  runs  much 
above  the  theoretical,  it  is  an  indication  that  steam  is  leaking  into  the 
cylinder  during  expansion.  If  it  runs  much  below,  a  leaky  exhaust 
valve  is  probable,  but  the  indication  should  be  regarded  only  as  an 
intimation  and  be  followed  out  by  an  investigation  of  the  engine  itself. 
The  actual  line  may  follow  the  plotted  curve  better  with  a  leaky  than 
with  a  tight  engine.  As  an  instance  of  this  may  be  shown  two  dia- 
grams taken  by  F.  Ruel  Baldwin,  from  an  engine  the  exhaust  valves 
of  which  leaked  very  badly.  The  first  of  these,  Fig.  61,  was  taken  while 
the  valves  were  in  their  leaky  condition,  but  the  expansion  curve  fits 
the  line  of  the  diagram  very  nicely.  Fig.  62  was  taken  after  the  valve 
had  been  made  tight,  but  there  is  a  considerable  difference  between 
the  theoretical  and  the  actual  lines. 

The  accompanying  transparent  chart  will  be-  found  convenient  in 
comparing  the  expansion  lines  of  actual  diagrams  with  the  theoretical 
curve.  Draw  upon  the  diagram  the  line  of  absolute  zero  14.7  pounds 
(or  whatever  the  barometric  pressure  may  have  been  at  the  time  it  was 
taken)  below  the  atmospheric  line,  and  the  clearance  line  locating  its 
position  by  calculation,  as  in  Fig.  55,  if  the  percentage  of  clearance  is 
known,  or  by  construction,  as  in  Fig.  60.  Place  the  diagram  beneath 
the  transparent  chart  with  the  zero  line  under  OX  and  the  clearance 
line  under  OA  and  the  theoretical  curve  may  be  studied  directly  or 
transferred  to  the  diagram  by  pricking  through  the  chart. 


CHAPTER  VIII 
THE  POINT   OF   RELEASE 

WHEN  it  is  possible  of  attainment  we  like  to  see  the  release  end  of 
a  diagram  given  the  appearance  shown  at  A  in  Fig.  63,  the  release 
occurring  early  enough  to  allow  the  pressure  to  fall  nearly  or  quite  to 
the  line  of  counter  pressure  by  the  time  the  end  of  the  stroke  is  reached. 
If  the  release  is  delayed  until  the  end  of  the  stroke  the  appearance 
will  be  more  like  that  indicated  at  B.  If  the  pressure  could  be  carried 
to  the  end  of  the  stroke  and  immediately  reduced  to  the  line  of  counter 
pressure,  as  indicated  by  the  outside  edge  of  the  black  space,  it  would 
be  advisable  to  retain  the  full  area;  but  since  some  area  must  be  lost 
here  in  expelling  the  exhaust,  it  is  better  that  it  should  be  above  the 
diagram,  as  at  A  than  below  as  at  B.  When  the  piston  is  approaching 
the  end  of  its  stroke,  it  has  come  to  be  a  question  of  stopping  it  and 
sending  it  in  the  other  direction.  To  do  this  smoothly  compression 
is  applied  on  the  other  side  of  the  piston,  and  obviously  there  is  no 
object  in  keeping  up  the  forward  pressure,  as  at  B,  unless-  we  can  add 
to  the  effective  area  of  the  diagram  (which  represents  the  useful  work 
done  by  the  steam)  by  doing  so.  It  is  therefore  better  to  let  the 
pressure  fall  off,  as  at  A,  assisting,  instead  of  opposing,  the  compression 
in  bringing  the  moving  parts  quietly  to  rest,  and  by  this  early  release 
removing  the  back  pressure  represented  by  the  black  portion  at  B,  so. 
that  the  piston  encounters  less  resistance  in  starting  upon  its  back- 
ward stroke  when  it  is  an  object  to  get  it  into  motion.  In  this  way 
nothing  is  sacrificed  in  the  area  of  the  diagram,  and  a  better  distribution 
of  the  pressures  with  reference  to  the  practical  work  of  the  engine  is 
obtained.  The  difficulty  of  attaining  the  result  on  most  engines  is  that 
where  the  lap  is  removed  from  a  valve  to  cause  it  to  open  early  and 
give  an  early  release,  this  very  lack  of  lap  retards  the  closure  and  does 
not  give  sufficient  compression.  On  the  Corliss  valve  this  may  be 
corrected  .by  setting  the  eccentric  ahead,  making  both  release  and  com- 
pression earlier,  but  disadvantages  attend  upon  too  great  an  angular 
advance  of  the  eccentric,  in  the  way  of  shortening  the  range  of  cut-off, 
and  the  advantages  of  the  valve  motion  in  quick  movement  at  admission, 
so  that  it  is  often  necessary  to  divide  the  difference  and  compromise  upon 

64 


THE   POINT  OF   RELEASE 


65 


a  point  like  that  shown  at  C.  The  benefit  of  an  early  release  is  very 
apparent  when  a  condenser  is  used,  for  with  an  early  release  and  a 
prompt  realization  of  the  vacuum,  as  at  D,  the  largest  possible  per- 
centage cf  the  load  is  thrown  upon  the  condenser;  while  a  tardy  release 
and  a  dragging  action  of  the  steam  in  leaving  the  cylinder  results  in 
the  loss  of  a  large  area  in  the  vacuum  portion  of  the  diagram  as  shown, 
by  the  shaded  portion  of  E,  calling  for  a  later  cut-off  and  more  steam. 

The  shape  of  this  end   of  the   diagram   depends  largely  upon   the 
amount  of  expansion  and  consequent  terminal  pressure.     If  the  steam 


D 


FIG.  63 


is  expanded  to  the  line  of  counter  pressure  the  diagram  will  terminate 
in  a  sharp  point  as  at  F,  and  at  the  end  of  the  stroke  the  cylinder  will 
be  full  of  steam  of  the  same  pressure  as  that  existing  in  the  exhaust 
pipe.  When  the  exhaust  valves  are  opened  there  is,  therefore,  no  flow, 
either  out  of  or  into  the  cylinder,  except  such  as  is  caused  by  the  move- 
ment of  the  piston.  When  the  cut-off  is  late  more  steam  is  admitted, 
and  has  to  be  expelled,  and  we  get  an  appearance  more  like  G\  and 
between  this  and  the  point  shown  at  F  there  may  be  any  variety  of 
shapes,  according  to  the  terminal  pressure  and  setting  of  the  valves. 


66  THE  STEAM  ENGINE   INDICATOR 

When  the  steam  is  cut  off  so  early  that  the  expansion  extends  below 
atmospheric  pressure,  or  the  pressure  against  which  the  engine  is  exhaust- 
ing, we  get  an  appearance  like  that  shown  at  ft.  Here  at  the  moment 
of  release  the  pressure  in  the  exhaust  pipe  is  greater  than  that  in  the 
cylinder,  and  when  the  valve  is  opened  at  a  there  is  an  inrush  of  the 
previously  exhausted  steam,  raising  the  pressure  to  the  counter-pressure 
line.  This  condition  is  apt  to  cause  a  disagreeable  slamming  of  the 
exhaust  valve,  which  is  lifted  from  its  seat  when  the  pressure  in  the 
cylinder  becomes  less  than  that  beneath  the  valve,  and  is  slammed  closed 
again  when  steam  is  admitted.  It  may  be  stopped  by  throttling  the 
initial  pressure  so  that  the  lessened  expansion  does  not  cause  a  loop. 

During  the  formation  of  this  loop  the  pressure  urging  the  piston 
forward  has  been  less  than  that  against  which  the  piston  moves,  the 
forward  motion  continuing  only  by  reason  of  the  momentum  of  the 
fly-wheel  and  moving  parts,  so  that  the  area  of  the  loop  represents  just 
so  much  work  exerted  against  the  piston,  and  must  be  subtracted  from 
the  other  area  of  the  diagram  to  get  at  the  effective  work.  This  point 
will  be  considered  in  detail  when  we  come  to  working  up  the  diagram 
for  power. 


CHAPTER   IX 
THE  COUNTER-PRESSURE   LINE 

THE  tendency  of  a  piston  to  move  depends  upon  the  difference  in 
pressure  upon  its  two  sides.  If  there  were  30  pounds  pressure  in  both 
ends  of  the  cylinder  at  once  the  piston  would  not  move  any  more  than 
though  there  were  no  pressure  at  all.  If  there  were  30  pounds  pressure 
on  one  side  and  15  pounds  on  the  other,  the  force  with  which  the  piston 
would  tend  to  move  would  be  the  same  as  though  there  were  15  pounds 
on  one  side  and  nothing  on  the  other.  In  other  words,  the  "effective" 
pressure  is  the  unbalanced  pressure,  or  the  difference  in  pressure  between 
the  two  sides. 

The  pressure  upon  the  piston  during  the  forward  stroke  is  repre- 
sented by  the  steam  and  expansion  lines,  the  pressure  in  the  same  end 
of  the  cylinder  during  the  backward  stroke  is  represented  by  the  exhaust-, 
counter-pressure,  or  back-pressure  line,  as  it  is  variously  called.  Obviously 
an  engine  will  be  doing  the  greatest  amount  of  work  when  the  pressure 
urging  the  piston  forward  is  greatest  and  the  retarding  effect  of  the  back 
pressure  is  least.  Steam  will  not  flow,  however,  from  one  place  to  another 
without  a  sufficient  difference  in  pressure  to  overcome  the  resistance  to 
movement  through  the  connecting  pipes  and  passages.  If  at  the  end 
of  the  stroke  the  steam  has  been  expanded  to  atmospheric  pressure  in  a 
non-condensing  engine,  there  will  be  no  immediate  outrush  of  steam 
from  the  cylinder  when  the  exhaust  valve  opens,  because  there  is  no 
greater  pressure  in  the  cylinder  than  that  of  the  atmosphere  into  which 
the  steam  must  flow.  The  steam  must  therefore  be  pushed  out  by 
the  piston,  and  the  resistance  to  its  movement  will  depend  upon  the 
velocity  with  which  it  flows  and  the  length  and  directness  of  the  exhaust 
pipe.  The  size  of  the  exhaust  pipe  and  passages  is  involved  in  the 
velocity  of  flow.  If  the  exhaust  pipe  were  as  large  as  the  cylinder  and 
directly  open  to  it  the  rate  of  flow  in  linear  feet  per  minute  would  be 
the  same  as  the  piston  speed.  If  the  area  of  the  pipe  or  the  passage 
leading  thereto  were  one-half  the  cross-sectional  area  of  the  cylinder 
the  rate  of  flow  would  be  twice  the  piston  speed,  because  to  get  through 
a  passage  of  one-half  the  area  in  the  same  time  the  steam  must  travel 
twice  as  fast.  As  the  resistance  to  flow  increases  with  the  velocity,  it 

67 


68 


THE   STEAM   ENGINE   INDICATOR 


is  found  desirable  to  limit  the  rate  of  flow  in  the  exhaust  passages  to 
6000  linear  feet  per  minute,  which,  for  a  piston  speed  of  600  feet  per 
minute,  requires  for  the  exhaust  passages  a  cross-sectional  area  of  one- 
tenth  that  of  the  cylinder.  For  other  piston  speeds  the  proper  area 
of  the  exhaust  passages  may  be  found  by  multiplying  the  cross-sec- 
tional area  of  the  cylinder  by  the  piston  speed  in  feet  per  minute  and 
dividing  by  6000. 

The  compression  of  the  steam  by  the  piston  pushing  it  out  of  the 
cylinder  against  the  resistance  to  flow  through  the  pipes  and  passages, 
will  show  on  the  indicator  diagram  in  raising  the  line  of  counter-pres- 
sure above  the  atmospheric  line  in  a  non-condensing  engine.  In  a  well- 


FIG.  64. 

proportioned  engine  at  moderate  piston  speeds  and  exhausting  through 
a  short  and  ample  exhaust  pipe  this  moving  pressure  will  not  be  notice- 
able with  an  ordinary  spring,  and  the  line  of  counter-pressure  will  merge 
into  the  atmospheric  line,  as  at  A,  Fig.  64.  Under  less  advantageous 
circumstances,  however,  the  back-pressure  line  will  be  elevated  above 
the  atmospheric  line,  as  at  B,  and  the  distance  between  them  will  be 
a  measure  of  the  force  required  to  overcome  the  resistance  to  the  out- 
flow of  the  exhaust. 

The  beginning  of  the  back-pressure  line  depends,  as  may  be  seen 
from  the  last  chapter,  very  much  upon  the  point  of  release  and  the  ter- 
minal pressure.  When  at  the  end  of  the  stroke  the  cylinder  is  full 
of  steam  of  a  high  pressure,  we  have  a  rapid  outflow  of  steam  as  soon 


THE  COUNTER-PRESSURE   LINE  69 

as  the  valve  is  opened  for  release,  but  even  with  the  greater  impelling 
pressure  a  sufficient  velocity  is  not  generated  to  discharge  this  greater 
volume  of  steam  (which  expands  when  the  pressure  is  reduced)  before 
the  piston  gets  some  distance  on  its  way  back,  making  the  beginning 
of  the  back-pressure  line  like  C;  and  sometimes  the  back  pressure  does 
not  reach  its  lowest  point  until  the  backward  stroke  is  practically  com- 
pleted, as  at  D. 

Sometimes  we  find  a  diagram  where  the  back-pressure  line  starts 
in  well  enough,  but  makes  a  gradual  rise  toward  the  center  of  the  dia- 
gram, falling  again  as  the  stroke  is  completed,  as  at  E.  This  may  be  caused 
by  too  great  velocity  in  the  middle  of  the  stroke,  either  from  contracted 
ports  or  too  much  inside  lap  on  a  slide  valve  narrowing  up  the  exhaust 
passage  as  the  center  of  the  stroke  is  reached,  and  where  the  piston, 
and  consequently  the  steam,  has  the  greatest  velocity.  The  same 
effect  may  be  produced  upon  a  Corliss  engine.  It  is  also  found  where 
a  pair  of  cylinders  working  on  cranks  set  at  90  degrees  exhaust  into  the 
same  pipe,  the  release  of  one  cylinder  occurring  practically  in  the  middle 
of  the  stroke  of  the  other  and  the  efflux  of  steam  into  the  pipe  causing 
a  rise  of  pressure. 

The  end  of  the  back-pressure  line  depends  for  its  shape  upon  the 
amount  of  compression.  At  c  in  diagram  B,  Fig.  64,  for  instance,  the 
exhaust -valve  closes  and  the  steam  remaining  in  the  cylinder  is  compressed, 
the  pressure  rising  upon  the  curve  shown.  With  no  compression  the 
back-pressure  line-  would  continue  straight  to  the  end  of  the  diagram, 
and  with  a  prompt  admission  we  should  have  a  square  corner  at  the 
end.  When  the  compression  commences  earlier  in  the  stroke  the  com- 
pression curve  runs  proportionally  higher,  as  is  well  shown  at  F,  taken 
from  an  engine  where  the  compression  varies  with  the  load,  and  showing 
the  effect  upon  the  counter-pressure  line  of  closing  the  exhaust  valve 
at  different  points  in  the  stroke.  It  is  even  possible  to  carry  the  pres- 
sure, by  compression  above  that  in  the  steam  chest,  so  that  when  the 
valve  opens  for  the  admission  of  steam,  the  pressure  in  the  cylinder 
being  greater  than  that  in  the  steam  chest,  there  is  a  drop  instead  of  a 
rise  to  the  line  of  realized  pressure,  as  shown  at  Q. 


CHAPTER  X 
THE  COMPRESSION  LINE 

COMPRESSION  is  the  inverse  or  opposite  of  expansion.  In  making 
the  expansion  line  the  volume  of  steam  admitted  up  to  the  point  of 
cut-off  is  increased  in  volume,  the  pressure  falling  in  an  inverse  ratio, 
and  we  remember  that  the  product  of  the  volume  and  pressure  was 
constant.  In  compression  the  volume  of  steam  inclosed  when  the  ex- 
haust-valve closes  is  diminished  in  volume  with  a  consequent  increase 
in  pressure,  and  in  this  case  too  the  product  of  the  volume  and  pres- 
sure is  constant.  If  we  compress  the  steam  into  half  the  space  which 
it  occupies  when  the  exhaust-valve  closes  we  shall  double  its  absolute 
pressure;  into  one-third  the  space,  treble  its  pressure,  etc.  The  clearance 
space,  being  in  most  cases  a  large  proportion  of  the  volume  inclosed, 
becomes  of  increased  importance. 

In  Fig.  65  suppose  the  exhaust-valve  to  close  at  0  and  the  clearance 
to  be  bounded  by  the  line  OA.  There  is  then  shut  into  the  cylinder 
when  the  exhaust  closes  a  volume  of  steam  proportional  to  the  line  08 
and  of  an  absolute  pressure  equal  to  8C.  When  the  piston  has  ad- 
vanced to  4  this  volume  will  be  one-half  of  08  and  the  pressure  will 
be  twice  8C:  so  at  6  the  volume  will  be  f  of  that  at  C  and  the  pressure 
I;  at  1  the  volume  will  be  J-  and  the  pressure  8  times  that  at  C.  The 
pressure  at  the  various  points  can  be  calculated  and  measured  upon 
the  ordinates  by  scale,  or  the  line  can  be  laid  out  graphically  for  the 
compression  line  by  any  of  the  methods  shown  for  the  expansion  line 
by  using  C  in  the  same  manner  that  the  point  of  cut-off  was  used  in  lay- 
ing out  the  expansion  line,  and  spacing  off  vertically  upon  the  line 
OA,  or  on  an  extension  of  8(7  instead  of  upon  08,  as  for  the  expansion 
line.  In  Fig.  65  the  curve  is  laid  out  by  the  method  described  in  Fig. 
55,  page  57.  It  is  rarely  that  it  is  of  service  to  apply  the  curve  to  the 
compression  of  an  actual  diagram  unless  it  is  from  a  single-valve  auto- 
matic engine,  where  under  light  loads  the  compression  line  becomes  nearly 
as  large  and  important  as  the  expansion.  It  will  be  remembered  that 
in  Fig.  60,  page  61,  it  was  shown  that  if  a  rectangle  was  constructed  upon 
the  expansion  line,  with  sides  parallel  and  perpendicular  to  the  atmos- 
pheric line,  its  diagonal  prolonged  would  cut  the  zero  line  OX  at  the 

70 


THE  COMPRESSION  LINE 


71 


intersection  of  the  line  OA  bounding  the  clearance.  This  is  equally 
true  of  the  compression  line,  and  it  will  be  seen  in  Fig.  65  that  the  diagonal 
OD  of  the  rectangle  abed  cuts  08  at  the  intersection  of  the  clearance 
line  OA.  In  Fig.  65  the  admission  valve  commences  to  open  at  about 
e,  and  as  the  piston  comes  to  a  standstill  merges  the  compression  into 
the  admission  line.  The  dotted  line  shows  where  the  pressure  would 
go  if  the  piston  advanced  further  into  the  clearance. 


It  is  difficult  for  some  engineers  to  understand  how  there  can  be 
compression  in  a  condensing  engine.  There  is,  they  reason,  a  vacuum 
in  the  cylinder  when  the  exhaust  valve  closes,  and  nothing  to  com- 
press. This  would  be  true  if  the  vacuum  were  complete,  but  the  "  vacuum  " 
of  practice  is  simply  an  absolute  pressure  less  than  that  of  the  atmosphere. 
The  less  the  absolute  pressure  the  more  complete  the  vacuum.  The 
pressure  of  the  atmosphere  is  equal  to  about  15  pounds  or  30  inches  of 
mercury.  When  we  have  a  vacuum  of  26  inches  we  have  still  in  the 
condenser  an  absolute  pressure  of  30  —  26=4  inches  of  mercury,  or  two 
pounds  available  for  compression. 

The  amount  of  pressure  or  the  effective  compression  obtained  by 
closing  the  exhaust-valve  does  depend,  however,  upon  the  tension  or 


72 


THE  STEAM  ENGINE  INDICATOR 


pressure  of  the  vapor  inclosed  in  the  cylinder  when  the  exhaust-valve 
closes.  Referring  to  Fig.  66,  suppose  we  have  an  engine  where  the 
clearance  space  OA  is  one-quarter  of  the  total  volume,  0(7  between  the 
piston,  cylinder  head,  and  valves  after  the  exhaust-valve  closes.  If 
the  counter-pressure  line  of  the  diagram  was  only  3  pounds  above  the 
line  of  absolute  zero,  corresponding  to  a  vacuum  of  24  inches,  there 
would  be  three  pounds  less  than  the  atmospheric  pressure  at  the  end 
of  the  stroke,  as  shown  at  a.  If  there  were  only  12  inches  of  vacuum 
or  9  pounds  absolute  to  start  the  compression  with  we  should  get  up 
to  21  pounds,  as  at  6.  With  a  non-condensing  engine  and  no  back 
pressure  (above  the  atmosphere)  we  should  get  45  pounds  by  com- 
pression, as  at  c,  while  with  6  gage  pounds  back  pressure  we  should 


6  Gauge  Pounds  =  21  Pounds  Absolute  Back  Pressure 


12~Inches  Vacuum  or  9  Pounds  Absolute  Back  Pressure 


24  Inches  Vacuum  or  3  Pounds  Absolute  Back  Pressure 


O       A 


Absolute  Zero  of  Pressure 

FIG.  66. 


get  up  to  69  pounds  above  the  atmosphere  with  the  same  valve  setting 
and  point  of  exhaust  closure  that  gave  3  pounds  less  than  atmospheric 
pressure  with  the  low  counter-pressure  line. 

The  smaller  the  clearance,  too,  the  greater  the  pressure  realized  by 
compression,  with  the  same  point  of  exhaust  closure,  on  account  of 
the  small  final  volume  possible.  In  Fig.  65,  with  the  clearance  AB, 
a  pressure  equal  to  e  was  realized.  If  we  had  half  the  clearance,  i.e., 
if  the  piston  could  have  advanced  to  F,  we  should  have  realized  a  pressure 
equal  to  /.  In  engines  with  a  variable  compression  it  is  necessary  to 
have  a  considerable  proportion  of  clearance  or  the  pressure  would  be 
excessive  with  the  early  exhaust  closure  usual  with  light  loads.  As  it 


THE   COMPRESSION   LINE 


73 


is,  the  pressure  generated  by  compression  frequently  exceeds  the  initial 
pressure  (see  diagram  G,  Fig.  64,  page  68). 

The  object  of  compression  is  initially  to  furnish  a  cushion  or  gradually 
increasing  resistance,  to  bring  the  moving  parts  to  rest  and  change  the 
direction  of  the  push  upon  them  without  t-he  shock  which  would  follow 
upon  the  sudden  opening  of  the  steam-valve.  In  Fig.  67  the  piston 
is  moving  to  the  right,  or  toward  the  shaft,  and  the  engine  is  about  in 
the  position  shown  in  the  small  sketch  between  the  diagrams.  Every 
joint  between  the  piston  and  the  main  crank  pin  is  in  compression,  and 
the  main  shaft  is  pushed  hard  against  the  outer  face  of  the  bearing. 
When  the  crank  reaches  the  center,  and  the  pressure  acts  on  the  other 
side  of  the  piston,  the  connecting  rod  will  pull  instead  of  push,  every 
joint  will  be  extended,  and  the  main  shaft  pulled  against  the  back  of 
the  bearing.  If  this  change  in  pressure  is  effected  suddenly  every  par- 
ticle of  lost  motion  in  every  joint  and  bearing  will  be  taken  up  with  a 


thump,  and  it  is  only  by  changing,  the  pressure  gradually  from  one  side 
to  the  other  that  we  can  make  it  run  smoothly.  When  the  piston  is 
at  the  point  in  the  stroke  indicated  at  al,  there  is  behind  it  the  pressure 
/c,  and  no  pressure  but  that  of  the  atmosphere  in  front  of  it.  As  it 
moves  along,  the  pressure  behind  it  decreases  while  at  d  the  pressure 
in  front  .of  ,it  begins  to  increase,  and  at  e  the  pressures  on  both  sides 
are  equal.  After  this  the  pressure  in  front  exceeds  that  behind  the 
piston,  but  the  change  is  gradual,  the  direction  of  thrust  is  changed 
under  a  slight  difference  of  pressure,  and  when  the  steam  is  admitted 
the  bearings  and  journals  are  already  firmly  pressed  against  the  surfaces 
upon  which  they  are  to  bear.  In  addition  to  the  steam  pressure  moving 
the  piston  forward  there  is  the  momentum  of  the  moving  parts  to  be 
reckoned  with. 

Aside  from  its  cushioning  effect  compression  has  another  advantage 
in  reducing  the  loss  from  clearance.  Take  an  exaggerated  instance. 
Suppose  an  engine  with  a  clearance  equal  to  100  per  cent,  i.e.,  that  the 


74 


THE   STEAM   ENGINE   INDICATOR 


volume  of  steam  required  to  fill  the  space  behind  the  piston,  including 
ports,  etc.,  when  the  engine  is  on  the  center,  is  equal  to  the  volume 
generated  by  the  piston's  movement,  i.e.,  the  piston  area  multiplied 
by  the  length  of  the  stroke.  It  is  understood  that  the  indicated  power 
is  in  proportion  to  the  inclosed  area  of  the  diagram.  Before  the  piston 
can  move,  the  clearance  must  be  filled  with  steam,  and  supposing  the 
engine  to  work  without  expansion,  it  would  take  two  cylinderfuls  of 
steam  to  do  the  work  of  one  stroke,  one  to  fill  the  clearance,  and  one 
to  supply  the  space  behind  the  moving  piston.  In  Fig.  68,  then,  there 
would  be  required  a  volume  of  steam  proportional  to  the  rectangle 
A  BCD  to  do  an  amount  of  work  proportional  to  the  rectangle  EFCD. 
Now  suppose  the  exhaust-valve  to  close  at  c  so  as  to  fill  the  clearance 
by  compression  with  steam  at  the  initial  pressure,  the  area  of  the 
diagram  has  been  reduced  by  the  amount  below  the  dotted  line,  but 


CLEARANCE 


FIG.  68. 

we  have  still  considerably  more  than  half  of  it  left,  and  as  the  clearance 
is  already  full,  have  used  only  half  the  volume  of  steam. 

Where  there  is  no  expansion  the  steam  required  to  fill  the  clearance 
space  is  a  dead  waste.  With  a  cut-off  engine  it  gets  a  chance  to  expand 
with  the  other  steam  and  does  some  good,  but  still  there  is,  theoretically, 
at  least,  a  saving  by  compression  and  for  the  abstract  case  unmodified 
by  such  practical  consideration  as  cylinder  condensation,  etc.,  the  greatest 
area  of  diagram  will  be  produced  by  a  given  volume  of  steam  when  the 
ratio  of  compression  equals  the  ratio  of  expansion,  i.e.,  when  the  clear- 
ance bears  the  same  relation  to  the  volume  at  the  commencement  of 
compression  that  the  volume  at  cut-off  does  to  the  volume  at  the  end 
of  the  stroke.* 

It  remains  only  to  consider  some  of  the  forms  obtained  in  practice. 
When  the  engine  is  of  a  type  in  which  the  compression  is  constant,  the 
best  results  will  generally  be  attained  under  normal  loads  by  having 
the  compression  round  up  nicely  into  the  admission  line,  as  at  a,  Fig.  69, 
meeting  the  perpendicular  line  at  about  one-third  of  its  height.  This 


*  See  Compression  as  a  Factor  in  Steam  Engine  Economy,  Proc.  A.S.M.E 
XIV,  189. 


Vol. 


THE   COMPRESSION    LINK 


75 


will  require  a  different  setting  of  the  exhaust-valve  for  different  heights 
of  the  counter-pressure  line,  as  explained  on  page  72,  and  can  be  deter- 
mined only  by  the  indicator.  If  no  indicator  is  used,  put  on  only  enough 
compression  to  make  the  engine  run  smoothly.  At  6  is  shown  excessive 
compression,  the  pressure  running  up  above  that  in  the  steam  chest, 
so  that  when  the  valve  opens  for  admission,  steam  flows  from  the  cylinder 
to  the  chest  and  the  pressure  falls.  A  form  of  compression  line  often 
met  which  is  shown  at  c,  where  the  pressure  instead  of  continuing  upward 
along  the  dotted  curve  falls  away  as  shown.  When  this  occurs  the  cause 
for  the  reduction  of  pressure  will  usually  be  found  in  a  leak.  As  the 
piston  approaches  the  end  of  its  stroke  its  movement  becomes  very  slow, 
the  volume  of  steam  involved  is  small  and  growing  smaller,  and  if  there 


FIG.  69. 

is  even  a  slight  leak  in  the  exhaust-valve,  drip- valve,  or  piston  there  will 
come  a  time  when  the  volume  of  steam  discharged  through  the  leak 
will  equal  the  volume  generated  by  the  movement  of  the  piston  in  the 
same  time.  To  state  it  more  simply,  at  all  times  the  pressure  will  be 
lower  than  if  there  were  no  leakage,  and  there  will  come  a  time 
when  the  escape  through  the  leak  with  the  increasing  pressure  will  pull 
the  pressure  down  as  fast  as  the  movement  of  the  piston  increases  it, 
and  the  line  will  become  horizontal  as  at  d,  or  it  may  even  fall  away 
as  at  e.  As  soon  as  the  pressure,  from  compression,  behind  the  piston 
becomes  greater  than  that  in  front  of  it  a  leak  in  the  piston  becomes 
effective  to  reduce  the  compression  pressure.  Such  a  diagram  as  Fig.  70, 
which  was  sent  to  the  author  for  explanation  as  to  the  formation  at  A, 
might  be  caused  by  a  badly  leaky  piston.  It  will  be  seen  that  the  com- 
pression rises  after  the  valve  closes  much  more  abruptly  than  it  should 


76 


THE   STEAM   ENGINE   INDICATOR 


have  done  at  that  distance  from  the  end  of  the  stroke.  This  would  be 
accounted  for  by  leakage  from  the  other  side,  where  the  pressure  is  still 
high,  into  the  confined  space  in  front  of  the  piston.  As  the  pressure 
behind  the  piston  decreases,  this  action  falls  off,  allowing  the  line  to  lean, 
and  after  the  release  occurs  on  the  other  end  the  leak  is  reversed,  from 
the  compression  space  into  the  other  end,  now  opening  to  the  exhaust, 
allowing  the  pressure  to  fall  off  as  shown.  It  is  probable,  as  the  exhaust 
closure  is  early  and  the  release  late  on  this  diagram,  that  a  diagram 
from  the  other  end  of  the  cylinder  would  show  opposite  conditions, 
early  release  and  little  compression,  which  would  locate  the  turn  in  the 
curve  about  where  it  occurs  in  the  diagram.  As  a  general  rule,  when 


;  FIG.  70. 

you  see  a  compression  line  falling  off  badly,  look  out  for  leaks.  Jt  is 
a  better  indication  than  a  failure  of  the  expansion  line  to  follow  the 
theoretical. 

It  is  a  matter  for  consideration,  however,  if  condensation  does  not 
play  an  important  part  in  the  formation  of  such  departures  from  the  regular 
curve.  The  surfaces  of  the  cylinder  head,  piston,  and  ports  have  just 
been  exposed  to  the  temperature  of  the  exhaust,  and  as  the  piston  iiears 
the  end  of  its  stroke  they  bear  a  large  proportion  to  the  small  volume 
of  steam  inclosed.  Enough  steam  must  be  condensed  upon  those  sur- 
faces to  bring  them  up  to  the  temperature  corresponding  to  the  pres- 
sure before  the  steam  can  remain  as  steam  in  contact  with  them,  and  this 
condensation  might  account  for  the  falling  off  in  pressure  necessary  to 
produce  these  deviations  from  the  true  curve. 


CHAPTER   XI 


MEASUREMENT    OF    THE    DIAGRAM    FOR    MEAN    EFFECTIVE 

PRESSURE 

ONE  of  the  principal" uses  of  the  indicator  diagram  is  to  determine 
the  horse-power  which  the  engine  is  developing.  One  of  the  important 
factors  in  this  problem  is  the  pressure  urging  the  piston  forward,  and  this 
can  be  found  with  any  accuracy  only  from  the  indicator  diagram.  The 


Diameter      24  inches 
Stroke  48  inches 

Revolutions  70. 
Scale  40. 


FIG.  71. 

-. 

pressure  varies  through  the  stroke,  and  is  opposed  by  a  varying  amount 
of  back  pressure,  so  that  the  average  unbalanced,  or,  as  it  is  commonly 
called,  the  "mean  effective  pressure,"  must  be  determined.  The  most 
elementary  way  of  doing  this  is  by  measuring  the  pressure  upon  the 
diagram  at  a  number  of  equidistant  points  and  taking  the  average. 
To  do  this,  divide  the  diagram  into  a  number  of  equal  parts  lengthwise, 
(ten  for  ordinary  work)  as  shown  in  Fig.  71  by  the  dotted  lines  and, 
with  a  scale  corresponding  to  the  spring  with  which  the  diagram  was 
taken,  measure  the  pressure  in  the  center  of  each  of  these  divisions; 
that  is,  upon  the  full  lines  or  ordinates.  Notice  that  this  pressure  must 
be  measured  between  the  lines  of  the  diagram,  as  from  a  to  6,  whether 

77 


78 


THE   STEAM   ENGINE   INDICATOR 


the  engine  is  condensing  or  non-condensing,  and  not  from  the  atmos- 
pheric or  any  other  line. 

Performing  this  operation  on  the  diagram  shown  in  Fig.  71  we  find, 
with  a  40-pound  scale,  87  pounds  on  the  line  or  "ordinate"  1;  89.5 
pounds  on  2;  65.5  on  3;  47  on  4;  37  on  5;  29.5  on  6;  23.5  on  7;  18.5 
on  8;  15  on  9;  and  12  on  10.  Adding  these  values  we  have  424.5  for 


the  sum,  and  dividing  by   10,  the  number  of  measurements,  find  the 
average  or  mean  effective  pressure  to  be  42.45  pounds. 

Several  expedients  may  be  resorted  to  for  shortening  the  labor  of 
dividing  the  diagram  and  locating  the  ordinates.  The  simplest  of  these 
is  to  have  a  rule,  a  little  longer  than  the  ordinary  length  of  your  diagrams, 
divided  as  shown  in  Fig.  73  just  as  you  want  your  diagram  to  be  divided, 


FIG.  73. 

with  nine  spaces  of  equal  length  in  the  middle,  the  two  end  spaces, 
0  to  1  and  10  to  0,  being  one-half  the  width  of  the  others.  Four  inches 
between  the  zero  marks  is  a  good  length  for  diagrams  from  3|  to  4  inches 
in  length,  and  one  each  of  3^  and  4^  inches,  with  a  short  one  for  the 
diagrams  from  small  cylinders,  will  cover  all  ordinary  cases. 

Draw  the  lines  OA  and  XB  at  the    extreme  ends   of    the  diagram 
and  perpendicular  to  the  atmospheric  line.     Place  the  rule  between  them, 


MEASURE   OF  THE   DIAGRAM   FOR  MEAN   EFFECTIVE   PRESSURE     79 

as  shown  in  Fig.  73,  at  such  an  inclination  that  both  zeros  come  upon 
the  perpendiculars.  Then  with  a  needlepoint  prick  the  card  opposite 
each  division  of  the  rule,  and  draw  the  ordinates  perpendicular  to  the 


FIG.  74. 


atmospheric  line  and  through  these  points.  An  engineer's  scale,  such 
as  that  referred  to  on  page  9  and  shown  in  Figs.  8  and  72,  may  be  used 
to  advantage  in  this  work.  If  the  diagram  is  just  4  inches  long 


FIG.  75. 

the  20-pound  divisions  of  the  50  scale  will  just  divide  it  into  ten  equal 
parts.  If  it  is  less  than  four  inches  incline  the  scale  as  in  Fig.  74,  so 
that  the  zero  is  upon  one  line  and  the  20  on  the  other.  The  figured 
divisions  will  divide  the  space  into  ten  equal  parts.  In  order  to  get  a 


80 


THE   STEAM   ENGINE    INDICATOR 


half  space  on  each  end  (that  is,  to  locate  the  ordinates  in  the  center  of 
the  equal  tenths),  slide  the  scale  to  the  position  shown  in  Fig.  75  so  that 
the  1  mark  is  on  one  line  and  the  21  mark  on  the  other.  Make  a  needle 
hole  or  pencil  mark  at  the  edge  of  the  scale  against  each  numbered  division 
and  erect  the  ordinates  square  with  the  atmospheric  line  and  passing 
through  the  points  indicated.  The  50  scale  works  very  well  down  to 
diagrams  3J  inches  in  length,  which  are  exactly  divided  into  tenths 
by  the  numbered  divisions  of  the  60  scale;  and  for  this  length  and  below, 
the  60  scale  will  preferably  be  used,  as  the  inclination  of  the  40  scale 
becomes  too  great.  For  diagrams  between  4  and  5  inches  the  40  scale 
is  used  in  the  same  way.  No  calculation  is  required.  If  the  diagram 
is,  on  trial,  too  long  for  the  50  scale,  use  the  40;  if  you  have  to  use  the 


FIG.  76. 

50  scale  at  too  much  of  an  angle,  use  the  60.     A  little  use  will  make 
the  process  perfectly  natural. 

The  principal  advantage  of  such  a  scale,  however,  especially  the 
12-  or  14-inch  scale,  is  in  measuring  the  length  cf  the  ordinates.  Usually 
the  pressure  on  each  ordinate  is  measured  with  the  minute  divisions 
of  the  common  scale,  the  ten  observations  added,  and  the  sum  divided 
by  ten  to  get  the  average.  Now  we  can  divide  by  ten  to  start  with 
by  dividing  the  value  of  the  scale  and  at  the  same  time  get  the  advantage 
of  the  coarser  reading.  With  a  40  spring,  instead  cf  calling  1  inch  40 
pounds,  suppose  we  call  it  4  pounds.  Then  we  can  measure  the  ordinate, 
add  the  results,  and  have  the  mean  effective  pressure  at  once.  The 
pound,  instead  of  being  ^  of  an  inch  will  be  J.  The  finest  divisions 
of  the  scale  will  represent  tenths  of  pounds  instead  of  full  pounds,  so 


MEASURE  OF  THE  DIAGRAM  FOR  MEAN  EFFECTIVE  PRESSURE     81 

that  they  can  be  read  much  more  accurately,  and  the  numbers  on  the 
scale  will  correspond  with  the  pound  marks.  Thus  in  Fig.  76  we  have 
on  the  ordinate  to  which  the  scale  is  applied,  10.5  pounds  pressure.  This 


FIG.  77. 


is,  of  course,  only  one-tenth  of  the  pressure  which  that  particular  ordinate 
represents,  but  we  shall  give  the  pressure  ten  records,  so  that  the  aggregate 
will  be  the  same  as  though  we  measured  each  on  the  given  scale  and  then 
divided  the  aggregate  by  ten.  v 


FIG.  78. 


There  are  also  procurable  from  the  instrument  makers  parallel  rules, 
as  shown  in  Figs.  77  and  78,  whose  method  of  application  is  too  obvious 
to  require  description. 


82 


THE   STEAM   ENGINE   INDICATOR 


Instead  of  measuring  each  ordinate  with  the  scale  corresponding  to 
the  spring  with  which  the  diagram  was  taken,  some  engineers  prefer 
to  lay  off  the  lengths  of  the  ordinates  continuously  on  the  edge  of  a 
strip  of  paper,  then  to  either  measure  the  whole  length  with  a  long  scale 
of  the  proper  unit,  or  with  a  scale  of  common  inches,  and  multiply  the 
length  by  the  scale  of  the  spring. 

In  the  measuring  of  the  mean  effective  pressure  by  ordinates  there 
remains  to  be  explained  the  treatment  of  diagrams  having  negative 
or  back-pressure  areas.  For  example,  in  Fig.  79,  after  the  point  a  is 


FIG.  79. 

passed,  the  forward  pressure  in  the  cylinder  is  less  than  the  back  pressure 
during  the  return  stroke.  The  piston  is  actually  hanging  back  upon 
the  engine,  and  the  loop  not  only  represents  no  addition  to  the  useful 
mean  effective  pressure,  but  a  force  acting  against  the  motion  of  the 
engine  equivalent  to  so  much  back  pressure.  The  average  pressure  of 
the  loop  portion  of  the  diagram  must  therefore  be  subtracted  from  that 
of  the  other  portion.  Erecting  the  ordinates  as  before  directed,  and 
measuring  with  a  40  scale,  we  have  98+93+40+20+5=256  as  the 
sum  of  the  measurements  in  the  main  portion  of  the  diagram,  and 
3+8  +  13  +  15  +  11=50  as  the  sum  of  the  measurements  in  the  loop. 
Taking  the  difference  and  dividing  by  10  to  get  the  average,  we  have 


256-50 
10 


'20.6  Ibs.  M.E.P. 


CHAPTER   XII 
THE   PLANIMETER 

THE  area  of  a  rectangle,  as  A,  B,  C,  D,  Fig.  80,  is  found  by  multi- 
plying its  height  by  its  length.  If  the  figure  shown  were  2  inches  high 
and  4  inches  long  it  would  obviously  contain  2X4=8  square  inches 
of  area.  If  on  the  other  hand  it  were  known  that  its  area  was  8  square 
inches  and  its  length  4  we  could  easily  tell  that  it  was  8 -=-4  =2  inches 
high.  If  we  wanted  to  know  how  high  it  would  be  if  it  were  any  other 
length  to  contain  the  same  area,  we  would  simply  divide  the  area  by 
the  new  length.  If  the  rectangle  in  Fig.  80  were  lengthened  to  8  inches 


— 4  inches 


Area  8  sq.  in. 


£C 


FIG.  80.  FIG.  81. 

it  could,  to  contain  the  same  area,  be  only  8-^-8  =  1  inch  high,  or  if 
lengthened  to  6  inches  8  -T-6=1J-  inches. 

Suppose  now  we  have  a  figure  like  Fig.  81,  and  wish  to  know  its 
average  height.  We  could  divide  it  into  a  number  of  rectangles,  as 
shown  by  the  dotted  lines,  and  find  the  height  which  each  rectangle 
would  be  if  extended  to  the  full  length,  of  the  diagram.  Supposing  the 
diagram  to  be  4  inches  long,  the  area  A  would  be  one-half  an  inch  high 
and  an  inch  long,  containing  therefore  one-half  a  square  inch  of  area. 
If  this  were  extended  to  4  inches  its  height  would  be  reduced  to  J-j-4=J 
of  an  inch.  The  area  B  is  2XJ  =  1  square  inch,  and  would  be  l-*-4=J 
of  an  inch  high  if  4  inches  long.  Similarly  C,  containing  1^  square 
inches,  would  be  lj-f-4=|  of  an  inch  high,  and  D,  already  4  inches  long, 
is  one-half  an  inch  high.  So  for  the  total  average  height  we  should 
have  J+J+J+i  =  l}  inches,  bringing  the  average  height  at  the  line  xy. 
That  this  is  right  is  evident  at  a  glance,  for  the  area  A  will  just  fill  the 
space  a,  and  that  part  of  B  which  is  above  the  line  xy  will  just  fill  the 

83 


84 


THE   STEAM   ENGINE   INDICATOR 


space  b  below  it.  But  if  we  know  in  the  first  place  the  area  of  the 
whole  figure  we  can  get  at  the  average  height  at  once  by  dividing  that 
area  by  the  length,  for  obviously  the  whole  is  equal  to  the  sum  of  all 
its  parts,  and  we  shall  get  the  same  result  by  dividing  the  whole  area 
by  4  as  by  dividing  each  of  its  parts  by  4  and  adding  the  quotients. 
Thus  the  whole  area  of  Fig.  81  is  ^  +  1+1^+2=5  square  inches,  and 
5^-4  =  1^,  the  same  as  the  sum  of  the  several  divisions. 

In  an  indicator  diagram  the  height  is  proportional  to  the  pressure, 
and  to  find  the  average  pressure  we  must  find  the  average  height.  We 
have  an  irregular  figure  which  we  wish  to  reduce  to  a  rectangle  of  the 
same  area  and  to  know  the  height  of  the  rectangle.  Imagine  the  diagram 
stepped  off  into  the  boundaries  of  rectangles,  as  in  Fig.  82,  and  it  will 


FIG.  83. 


be  clear,  in  view  of  what  has  been  said  about  Fig.  81,  that  dividing  its 
area  by  its  length  will  give  its.  average  height;  and  inasmuch  as  this 
is  true  however  fine  the  divisions  or  steps,  we  may  imagine  them  to  be 
so  fine  as  to  be  included  in  the  width  of  the  line  which  bounds  the 
diagram,  and  arrive  at  the  fact  that  the  area  of  an  indicator  diagram, 
or  any  other  plane  figure  for  that  matter,  divided  by  its  length  equals 
its  average  height. 

Fortunately  a  means  is  at  hand  for  easily  and  accurately  measuring 
the  area  of  such  diagrams.  The  planimeter,  the  instrument  used  for 
this  purpose,  is  made  in  a  variety  of  forms,  and  is  cold  at  prices  ranging 
from  five  to  thirty-five  dollars.  The  Amsler  was  the  first  upon  the 
market,  and  as  a  typical  example  is  shown  in  Fig.  83.  It  consists  of 
two  arms  pivoted  at  the  top,  upon  one  of  which  is  carried  a  roller  free 


THE   PLANIMETER 


85 


to  revolve  upon  an  axis  parallel  to  the  arm  itself.  The  roller  is  divided 
circumferentially  into  ten  equal  parts,  each  of  which  represents  a  square 
inch  of  area,  and  each  of  these  parts  is  further  divided  into  equal  parts 
representing  each  one-tenth  of  a  square  inch,  as  shown  in  Fig.  84.  Close 
to  the  edge  of  the  roller  is  a  stationary  plate  having  the  same  curvature- 
and  containing  a  vernier  made  by  dividing  a  space  nine-tenths  as  long 
as  one  of  the  large  divisions  of  the  roller  into  ten  equal  parts. 

In  Fig.  85  let  the  space  between  A  and  B  represent  one  of  the  larger 
divisions  of  the  wheel,  and  the  space  between  C  and  D  the  vernier. 
In  reading  the  instrument  take  the  number  on  the  wheel  which  has 
passed  the  zero  mark  of  the  vernier  when  the  wheel  is  turning  to  the  left 
as  indicated  by  the  arrow,  as  the  number  of  whole  square  inches,  in 
this  case  6.  The  tenths  of  a  square  inch  are  indicated  by  the  number 
of  spaces,  such  as  a,  which  have  passed  the  zero  mark,  in  this  case  1; 
so  that  the  reading  of  the  scale  as  laid  down  in  Fig.  85  is  6.1  square  inches. 


10 


1234  67 

f   I    I  1 


8      9 


bed 


FIG.  84. 


FIG.  85. 


Since  the  vernier  CD  is  nine-tenths  as  long  as  AB  each  division  of  the 
vernier  must  be  nine-tenths  of  each  division  of  the  scale.  From  0  to 
1  on  the  vernier  is  nine-tenths  of  the  space  beneath  it  on  the  wheel,  then 
the  space  between  the  line  b  on  the  wheel  and  the  line  1  on  the  vernier 
is  just  one-tenth  of  one  of  the  spaces  such  as  a  upon  the  roller,  the  space 
between  the  lines  2  and  c  is  just  two-tenths,  between  3  and  d  three- 
tenths,  etc.  If,  then,  the  wheel  rolls  in  the  direction  of  the  arrow 
one-tenth  of  one  of  the  spaces  o,  corresponding  to  an  area  of  one  one- 
hundredth  of  a  square  inch,  the  lines  1  and  b  will  coincide,  for  two  one- 
hundredths  2  and  c  would  coincide,  so  that  we  get  the  hundredths  of  a 
square  inch  by  writing  that  number  on  the  vernier  which  is  opposite 
any  line  on  the  wheel.  For  instance,  in  reading  the  instrument  as  it 
stands  in  Fig.  84  write,  first,  the  number  on  the  wheel  to  the  left  of  the 
zero  mark,  in  this  case  4;  then  the  number  of  whole  spaces  between 
that  number  and  the  zero  mark,  in  this  case  7;  and  last  the  number 
on  the  vernier  which  is  in  line  with  a  mark  on  the  wheel,  in  this  case  3. 


86 


THE   STEAM   ENGINE   INDICATOR 


The  whole  reading  therefore  is  4.73  square  inches,  the  decimal  point 
being  placed  after  the  4,  the  7  and  3  being  tenths  and  hundredths  as 
before  explained.  It  will  be  noticed  that  only  the  zero,  5,  and  10,  are 


FIG.  86. 

numbered  on  the  vernier  in  Fig.  84,  and  this  is,  the  case  in  the  actual 
instrument,  the  intermediate  marks  being  easily  known  by  their 
position. 


FIG.  87. 


The  eye  soon  becomes  accustomed  to  quickly  determining  the  mark 
upon  the  vernier  which  coincides  with  one  upon  the  wheel,  the  marks 
at  either  side  of  it  being  just  within  the  marks  upon  the  wheel,  giving 
the  arrangement  shown  at  A  in  Fig.  84. 


THE   PLANIMETER 


87 


The  plammeter  should  be  used  upon  a  smooth  but  not  slippery  sur- 
face, such  as  that  of  heavy  drawing  paper  or  Bristol  board.  Place  a  sheet 
of  this  large  enough  to  include  the  planimeter  and  the  diagram  upon 
the  drawing  board,  and  fasten  it  with  thumb  tacks.  Set  the  stationary 
point  of  the  pianimeter  into  the  paper  in  such  a  position  that  the  tracing 
point  can  be  carried  around  the  outline  of  the  diagram  without  bringing 
the  wheel  into  contact  with  the  edge  of  the  paper.  The  instrument 
can  be  worked  to  the  best  advantage  when  it  is  neither  allowed  to  close 
up  too  closely,  as  in  Fig.  86,  nor  to  extend  too  widely,  as  in  Fig.  87.  A 
better  position  for  the  stationary  point  than  either  of  these  is  shown 
in  Fig.  88,  the  motion  of  the  roller  being  easiest  when  the  arms  are 
near  a  right -angular  position.  When  the  areas  to  be  measured  are  large, 
or  when  there  is  considerable  space  between  the  top  of  the  diagram 
and  the  top  edge  of  the  card,  contact  of  the  roller  with  the  edge  of  the 


FIG.  88. 

card  may  be  avoided  by  inverting  the  diagram,  as  indicated  by  the 
dotted  diagram  in  Fig.  88,  using  the  planimeter  always  in  the  same 
direction,  that  in  which  the  hands  of  a  watch  run;  for  obviously  the 
area  of  the  diagram  remains  the  same  in  whatever  position  the  card  is 
placed. 

Place  the  tracing  point  on  any  convenient  point  in  the  line  of  the 
diagram  and,  by  pressing  upon  it,  make  an  incision,  to  mark  the  point 
of  starting.  Take  the  reading  of  the  instrument  as  it  stands,  then  with 
the  tracing  point  follow  the  line  of  the  diagram  in  the  direction  in  which 
the  hands  of  a  watch  move,  as  indicated  by  the  arrows  in  Figs.  89  and 
90.  Follow  the  line  as  made  by  the  pencil,  not  necessarily  in  direction 
(for  on  a  right-handed  diagram,  as  in  Fig.  89,  you  will  have  to  trace 
in  the  opposite  direction  from  that  of  the  pencil  which  made  it,  in  order 
to  carry  the  tracing  point  in  the  direction  of  the  hands  of  a  watch) ,  but 


88 


THE  STEAM  ENGINE   INDICATOR 


in  course.  For  instance,  in  Fig.  79,  do  not  leave  the  expansion  line  at 
a  and  run  out  on  the  back-pressure  line,  but  follow  the  diagram  naturally 
all  the  way  around,  as  the  arrows  indicate,  and  as  it  was  drawn  by  the 
pencil;  and  in  Figs.  89  and  90  do  the  same,  although  in  tnis  case  you 
will  trace  the  diagram  backward  from  the  direction  in  which  the  pen- 
cil went  over  it.  If  the  pointer  traces  in  the  opposite  direction  to  the 
hands  of  a  watch  the  wheel  will  take  out  the  area  instead  of  adding  it. 
In  Fig.  79  we  saw  that  the  area  of  the  loop  was  negative,  and  that  it 
needed  to  be  subtracted  from  the  other  apart  of  the  diagram  to  get  the 
mean  effective  pressure.  It  will  be  seen  that  by  following  the  lines  of 
the  diagram  as  directed  the  tracing  point  of  the  planimeter  will  pass 
around  the  negative  portions  of  the  diagram  in  a  direction  contrary 
to  the  hands  of  a  watch,  and  that  therefore  these  areas  will  be  automat- 
ically subtracted.  In  this  connection,  be  careful  when  starting  to  trace 
a  diagram  with  loops,  to  move  the  tracing  point  in  a  direction  that  will 


FIG.  89. 


FIG.  90. 


carry  it  with  the  hands  of  a  watch  over  the  main  portion  of  the  diagram, 
If  Fig.  90,  for  instance,  were  started  at  the  point  a  or  anywhere  within 
one  of  the  loops  the  first  movement  of  the  tracing  point  would  have  tc 
be  in  the  opposite  direction  from  that  of  the  hands  of  a  watch. 

Having  traced  around  the  diagram  and  brought  the  pointer  around 
and  into  the  hole  from  which  it  started,  take  the  reading  in  the  ne\v 
position,  subtract  from  the  reading  in  the  starting  position,  and  the 
difference  will  be  the  area  of  the  figure  traced.  If  the  roller  were 
placed  at  zero  to  start  with,  the  reading  would  give  the  area  at  once 
but  it  is  easier  to  take  the  instrument  as  it  stands  and  subtract  the 
initial  reading.  Suppose  we  start  with  the  wheel  at  1.42,  and  aftei 
tracing  the  diagram  find  the  reading  to  be  4.69,  then  the  area  will  be 
4.69—1.42=3.27  square  inches.  Now  to  prove  the  work,  trace  the 
diagram  again,  write  the  result  above  the  former  reading,  again  take 


THE   PLANIMETER 


89 


the  difference,  and  if  the  work  has  been  accurate  the  last  reading 
should  be  7.96.  If  we  run  around  still  again  the  reading  would  be  1.23. 
This  value  would  really  be  11. 23,  as  we  started  from  7.96  and  added 
3.27  inches,  but  as  the  capacity  of  the  wheel  is  limited  to  10  inches,  we 
have  to  understand  the  addition  in  the  tens  column  and  simply  borrow 
one  when  we  subtract  the  7.96.  The  readings  are  as  follows: 

11.23 

7.96=3.27 
4.69=3.27 
1.42=3.27 

The  three  readings  agreeing,  we  may  feel  certain  that  our  work  has 
been  correctly  done  and  that  the  area  of  the  diagram  is  3.27  square  inches. 
By  dividing  this  area  by  the  extreme  length  the  average  height  is  found. 

To  measure  the  length  of  the  diagram,  draw  lines  as  ab}  cd,  Fig.  91, 
perpendicular  to  the  atmospheric  line  and  touching  the  extreme  end 
of  the  diagram.  No  matter  what  the  shape  of  the  diagram  may  be, 
no  portion  of  its  line  must  extend  outside  of  these  perpendiculars,  which 


FIG.  91 

must,  however,  touch  the  diagram  at  both  ends.  When  two  diagrams 
are  taken  on  one  card,  however,  remember  that  you  want  the  length 
of  each  diagram,  not  the  extreme  length  between  both,  as  shown  in  Fig. 
91.  Now  measure  the  horizontal  distance  between  these  vertical  lines. 
This  is  very  handily  done  with  the  50  scale  of  the  6-inch  triangular 
scale,  each  50th  being  equivalent  to  0.02,  so  that  the  length  may  be  ex- 
pressed directly  in  decimals. 

Divide  the  area  as  found  by  the  planimeter  by  the  length,  and  multiply 
the  quotient  by  the  scale  of  the  spring  ivith  which  the  diagram  was  taken. 
The  product  will  be  the  mean  effective  pressure. 

In  a  planimeter  the  length  of  the  tracing  arm  multiplied  by  the 
movement  of  the  wheel  equals  the  area  traced.  If  in  Fig.  92  the  length 
of  the  tracing  arm  (the  distance  between  the  tracing  point  and  the  hinge) 


90 


THE  STEAM  ENGINE   INDICATOR 


is  4  inches,  the  circumference  of  the  roller  must  be  2.5  inches  in  order 
that  one  revolution  may  equal  10  square  inches.  Inversely  the  wheel 
movement  equals  the  area  divided  by  the  length  of  the  tracing  arm. 
If  with  the  wheel  having  a  circumference  of  2.5  inches  we  used  a  tracing 
arm  5  inches  long  instead  of  4  inches,  in  tracing  an  area  of  10  square 
inches  the  wheel  would  not  turn  a  full  revolution.  Its  circumferential 
movement  would  have  to  be  only  2  inches  in  order  that  that  movement 
multiplied  by  the  length  of  the  arm  might  still  be  equal  to  the  area,  10. 
The  movement  of  the  wheel,  and  thus  the  reading,  is  inversely  propor- 
tional to  the  length  of  the  arm.  If  the  length  of  the  arm  is  doubled  the 
reading  will  be  halved.  If  the  arm  is  one-third  as  long  the  reading  will 
be  three  times  as  large,  etc.  It  has  been  explained  that  to  get  the  mean 
effective  pressure  the  area  must  be 
divided  by  the  length  of  the  dia- 
gram. If  the  diagram  were  twice 
as  long,  with  a  given  area  the  mean 
effective  pressure  would  be  half  as 
much.  In  other  words  the  mean 
effective  pressure  varies  inversely 
as  the  length  of  the  diagram.  Since 
the  reading  varies  inversely  as  the 
length  of  the  arm,  and  the  mean 
effective  pressure  varies  inversely 


FIG.  92. 

as  the  length  of  the  diagram,  we  can,  by  making  the  length  of  the  arm 
equal  to  the  length  of  the  diagram,  make  the  reading  proportional  to 
the  mean  effective  pressure.  Suppose  an  instrument  with  an  arm  of 
4  inches  and  a  wheel  having  a  circumference  of  2.5  inches.  One  revo- 
lution of  the  wheel  will  mean  10  square  inches.  Suppose  it  is  applied 
to  a  diagram  3  inches  long  and  registers  3.75  square  inches  area.  If  the 
diagram  was  taken  with  a  40  spring  the  mean  effective  pressure  would  be 


Area  X  scale     3.75X40 


Length 


3 


50lbs. 


THE   PLANIMETER 


91 


Suppose  now  we  adjust  the  length  of  the  arm  so  that  it  equals  the 
length  of   the  diagram,  3    inches,  the  reading  will  then   be    J   of  what 

4X3  75 
it  was  before  or  -  =5.00  and  by  shifting  the  decimal  point  we  have 

o 

at  once  50  pounds.     Changing  the  length  of  the  arm  performed  me- 


FIG.  93. 


chanically  the  division  before  required.  For  a  40  scale,  therefore,  this 
instrument  will  give  us  at  once  on  the  wheel  the  mean  effective  pressure 
and  for  other  scales  the  pressure  can  be  taken  proportionally;  one-half 
for  a  20  scale,  three-fourths  for  a  30,  five-fourths  for  a  50,  etc.  An  Ams- 


FIG.  94. 

ler  planimeter  with  an  adjustable  tracing  arm  is  shown  in  Fig.  92.  The 
length  of  the  diagram  is  taken  between  the  two  points  M  and  N,  which 
are  always  the  same  distance  apart  as  the  tracing  point  A  and  the  joint 
C  upon  which  it  hinges. 

In   another   type   of   planimeter    the    reading   is   indicated    by   the 
sidewise  movement  of  the  wheel  read  against  a  contiguous  scale  as  in 


92  THE   STEAM   ENGINE   INDICATOR 

Fig.  93,  or  upon  the  shaft  upon  which  it  slides  as  in  Fig.  94.  As  these 
scales  are  changeable  and  the  arms  adjustable,  the  mean  effective  pres- 
sure can  be  read  direct  for  any  scale  or  length  of  diagram.  The 
instrument  shown  in  Fig.  92  can  be  set  to  read  directly  in  horse-power 
by  making  the  length  of  the  arm  equal  to 

Length  of  diagram  X  40  X  33000 


Scale  X  revs,  per  min.  X  area  X  stroke' 

in  whfch  the  stroke  should  be  taken  in  feet.  Instruments  like  those 
shown  in  Figs.  93  and  94,  in  which  a  scale  corresponding  to  that  of  the 
diagram  can  be  used  to  measure  the  wheel  movement,  can  be  set  to  read 
directly  in  horse-po'wer  by  making  the  length  of  the  tracing  arm  equal  to 

Length  of  diagram  X  33000 
Revs,  per  min.  X  area  X  stroke* 

If  this  gives  an  impracticable  length  of  arm  the  required  length  can  be 
multiplied  or  divided  by  a  number  which, will  make  it  practicable  and 


FIG.  95. 

the  reading  multiplied  or  divided  by  the  same  number.  If,  for  instance, 
the  formula  called  for  an  arm  of  1.5  inches  it  would  be  better  to  have  the 
arm  3  inches  and  multiply  the  reading  by  2. 

A  home-made  planimeter  with  which  it  is  possible  to  do  quite  accurate 
work  may  be  made  by  bending  a  piece  of  wire  as  in  Fig.  95,  flattening 
and  sharpening  into  a  knife  edge  the  end  at  B  and  pointing  the  end 
at  A.  The  distance  AB  should  be  10  inches. 

Locate  roughly,  by  judgment,  the  geometrical  center  of  the  figure, 
its  center  of  gravity,  so  to  speak;  the  point  upon  which  it  would  balance 
if  cut  out  of  cardboard  as  in  Fig.  96.  In  -the  indicator  diagram,  Fig. 
97,  this  point  would  be  at  about  A.  Draw  the  line  AB}  connecting  the 
center  with  any  point  upon  the  circumference,  set  the  planiraeter  arm 
roughly  at  right  angles  with  A  B,  and  press  the  knife  edge  lightly  into 
the  paper  to  mark  the  point  of  starting  as  at  X.  Carry  the  tracing 
point  out  over  AB  and  around  the  diagram  in  the  direction  that  a  clock 
runs  as  indicated  by  the  solid  arrows  and  back  over  A  B,  making  another 
depression  as  at  Z  to  mark  the  position  of  the  knife  edge  when  the  trac- 
ing point  is  again  at  the  center  A.  Then  being  careful  to  move  neither 


UNIVERSITY 

OF 


THE    PLANIMETER 


93 


the  tracing  point  nor  the  knife  edge,  revolve  the  diagram  180°,  using 
the  tracing  point  as  a  center,  bringing  it  into  the  dotted  position  of  Fig. 
97.  Having  secured  the  diagram  in  this  position  trace  it  again  in  the 
opposite  direction  from  that  followed  by  the  hands  of  a  watch  as  shown 
by  the  dotted  arrows,  and  make  still  another  depression  to  mark  the 
position  of  the  knife  edge  when  the  tracing  point  returns  to  the  center. 
This  will  probably  be  somewhere  near  .Y,  as  at  F.  We  have  now  three 
marks:  X,  that  at  which  the  knife  edge  started;  Z,  that  to  which  it  de- 
parted; and  F,  that  to  which  it  returned  when  the  diagram  was  retraced. 


FIG.  96. 


For  plainness  I  have  reproduced  them  at  the  left.  Make  a  mark  as 
" ab"  half  way  between  XY,  then  the  distance  between  this  mark  and 
Z,  i.e.,  the  length  of  the  dotted  line,  multiplied  by  the  length  of  the 
planimeter  arm  AB,  Fig.  95,  will  be  the  area  in  square  inches  approxi- 
mately, and  the  approximation  will  be  very  close  when  the  arm  is  of 
considerable  length  compared  with  the  area  to  be  measured.  By  making 
the  planimeter  arm  10  inches  in  length  the  multiplication  may  be  done 
by  shifting  the  decimal  point,  or  as  each  inch  of  length  will  indicate  10 
square  inches  the  area  may  be  measured  directly  by  taking  the  distance 
ZX  with  a  scale  of  10  to  the  inch,  each  tenth  representing  10  square 


94 


THE   STEAM  ENGINE   INDICATOR 


inches,  or  a  scale  of  100  to  the  inch,  each  unit  of  which  would  repre- 
sent one-tenth  of  a  square  inch. 

The  function  of  the  other  arm  of  the  planimeter,  one  end  of  which 
is  stationary,  is  simply  to  guide  the  hinged  end  in  a  definite  path.  This 
end,  otherwise  hinged,  may  be  guided  by  a  straight  groove  as  in  Fig.  99. 

In  Fig.  98,  start  with  the  tracing  point  at  A  and  the  wheel  at  zero 
and  trace  the  rectangle  A  BCD.  The  wheel  motion  gained  in  moving 
from  A  to  B  is  neutralized  by  the  movement  from  C  to  D.  The  line 
BC  is  in  the  neutral  axis,  so  the  wheel  gets  no  movement  while  the  tracer 
passes  over  it.  When  the  point  arrives  at  D,  therefore,  the  wheel  will 
have  returned  to  zero,  and  the  full  area  of  the  rectangle  will  be  recorded 
while  the  tracing  point  passes  down  the  line  DA.  For  a  rectangle,  there- 


FIG.  1)8. 


FIG.  99. 


fore,  with  its  left-hand  edge  in  the  neutral  line  of  the  instrument,  all 
that  is  necessary  to  find  the  area  is  to  start  at  the  upper  right-hand 
corner  with  the  wheel  at  zero  and  carry  the  tracing  point  down  the  right- 
hand  edge,  as  DA  in  Fig.  98.  Conversely,  if  we  have  a  given  area  re- 
corded on  the  wheel,  we  can  find  the  height  of  a  rectangle  of  equal  area 
for  a  given  length  by  running  the  tracing  point  up  the  line  marking 
its  right-hand  edge  (the  left  being  in  the  neutral  line),  until  the  wheel 
returns  to  zero.  Suppose,  for  instance,  we  start  at  A,  Fig.  98,  with 
the  planimeter  wheel  at  zero  and  trace  the  outline  of  the  indicator  diagram. 
When  the  tracing  point  gets  around  to  A  again  the  area  of  the  diagram 
will  be  recorded  on  the  wheel.  Now,  suppose  we  run  the  tracing  point 
up  the  line  AD  until  the  wheel  comes  back  to  zero,  the  line  AD  will  be 
the  average  height  of  the  indicator  diagram,  that  is  the  height  of  a  rectangle 


THE   PLANIMETER  95 

of  equal  area,  and  by  measuring  the  length  of  AD  with  the  scale  correspond- 
ing to  the  spring  with  which  the  diagram  was  taken,  we  find  the  mean 
effective  pressure  of  the  diagram  at  once  without  calculation. 

This  principle  is  made  use  of  in  the  Coffin  averaging  instrument, 
a  form  of  planimeter  especially  adapted  to  measuring  the  mean  effective 
pressure  represented  by  indicator  diagrams  and  shown  in  Fig.  99.  The 
indicator  card  is  placed  under  the  clips  A  and  C,  with  the  atmospheric 
line  parallel  with  the  horizontal  leg  of  the  stationary  clip  C,  and  the 
left-hand  edge  of  the  diagram  against  the  inside  vertical  edge  of  that 
clip.  The  inside  edge  of  the  movable  clip  A  is  then  placed  against  the 
right-hand  extremity  of  the  diagram,  so  that  the  length  of  the  diagram 
is  just  included  between  the  two  clips.  The  tracing  point  of  the  plan- 
imeter is  then  placed  upon  any  portion  of  the  diagram  which  is  against 
the  right-hand  clip,  the  wheel  set  to  zero  and  the  point  gently  pressed 
into  the  paper  to  mark  the  starting  point.  The  tracing  point  is  then 
carried  around  the  diagram  in  the  direction  of  the  hands  of  a  watch, 
and  when  it  returns  to  the  point  from  which  it  started  the  area  of  the 
diagram  will  be  recorded  upon  the  wheel.  No  attention  need  be  paid 
to  this  reading.  Simply  carry  the  point  upward  against  the  edge  of  the 
clip  A  until  the  wheel  returns  to  zero,  at  which  point  press  the  tracer 
again  into  the  paper.  The  distance  between  the  starting  point  and  the 
point  thus  made  will  be  the  average  height  of  the  diagram  and  measured 
with  the  scale  of  the  spring  with  which  the  diagram  was  taken  will  give 
at  once  the  mean  effective  pressure.  It  is  not  necessary  even  to  set  the 
wheel  at  zero  in  starting.  You  can  record  the  reading,  whatever  it  may 
be,  after  the  tracer  has  been  set  at  the  starting  point,  trace  the  diagram 
and  then  run  the  tracing  point  upward  beside  the  clip  until  the  wheel 
returns  to  the  reading  with  which  you  started.  The  whole  apparatus 
is  mounted  on  a  rosewood  board  with  an  inset  tablet  of  suitable  surface 
for  the  planimeter  wheel  to  run  upon.  A  weight  Q  is  placed  upon  the  end 
opposite  the  tracing  point  to  hold  it  in  the  guiding  groove. 


CHAPTER   XIII 
COMPUTING  THE  HORSE  POWER 

FORCE  is  that  which  tends  to  produce  motion  or  change  of  motion 
in  matter.  The  pressure  of  steam  or  of  water  under  a  head,  the  pull 
of  a  weight,  the  pull  or  push  of  a  muscle,  are  all  familiar  examples  of 
force. 

When  force  is  exerted  through  space,  Work  is  done.  The  full  steam 
pressure  may  stand  upon  the  engine  piston  for  hours,  but  no  work  will 
be  done  unless  the  piston  moves.  A  suspended  weight  does  no  work 
except  while  it  is  being  lowered,  and  it  is  only  in  its  ability  to  be  lowered, 
i.e.,  in  its  elevated  position,  that  its  capacity  for  doing  work  exists. 

The  Foot-Pound  is  the  unit  of  work  or  energy.  It  is  the  equivalent 
of  1  pound  of  force  exerted  through  1  foot  of  space.  To  lift  100 
pounds  1  foot  would  require  100  foot-pounds  of  energy,  as  it  would 
also  to  lift  1  pound  100  feet.  If  a  horse  has  to  pull  50  pounds  to  draw 
a  wagon,  and  draws  it  100  feet,  he  will  develop  5000  foot-pounds. 
Notice  that  this  has  no  reference  to  the  Weight  of  the  wagon,  simply  to 
the  force  required  to  drag  it. 

A  Horse-Power  is  the  unit  of  the  rate  of  development,  or  of  consump- 
tion of  energy  or  of  work.  It  is  550  foot-pounds  per  second,  33,000  foot- 
pounds per  minute,  or  1,980,000  foot-pounds  per  hour. 

The  indicator  gives  us  a  means  of  determining  the  average  force 
pushing  the  piston  (the  mean  effective  pressure  per  square  inch  multi- 
plied by  the  number  of  square  inches  in  the  piston),  and  this  multiplied 
by  the  number  of  feet  through  which  the  piston  moves  in  a  minute  and 
divided  by  33,000  will  give  the  horse-power  which  the  engine  is  developing. 

The  simplest  formula  for  horse-power  is,  therefore, 

_  Area  XM.E.P.X  piston  speed 
33000 

The  area  of  the  piston  is  found  by  multiplying  the  square  of  the 
diameter  of  the  cylinder  by  0.7854.  Table  I  at  the  end  of  the  volume 
renders  this  calculation  unnecessary. 

The  mean  effective  pressure  (M.E.P.)  is  found  by  measurement 
from  the  diagram,  as  explained  in  the  previous  chapter. 

96 


COMPUTING  THE   HORSE-POWER  97 

PISTON  SPEED 

The  piston  speed  in  this  sense  is  the  number  of  feet  through  which 
the  pressure  acts  upon  the  piston  per  minute.  In  a  double-acting 
engine,  (that  is,  an  engine  which  takes  steam  at  each  stroke,  or  twice 
a  revolution)  this  is  the  revolutions  per  minute  X  2  X  the  length  of  the 
stroke  in  feet.  If  the  engine  is  single-acting,  but  takes  steam  every  revolu- 
tion, the  piston  speed  is  the  product  of  the  revolutions  per  minute  and 
the  stroke  in  feet.  Gas  engines  of  the  4-cycle  type  make  a  working 
stroke  once  in  two  revolutions,  and  their  piston  speed  when  this  is  done 
is  the  stroke  in  feet  times  one-half  the  revolutions  per  minute;  but 
when  the  governing  is  accomplished  by  the  hit  and  miss  method,  their 
piston  speed  can  be  determined  only  by  counting  the  explosions,  the 
piston  speed  being  the  stroke  in  feet  multiplied  by  the  number  of  explo- 
sions per  minute. 

Notice  that  "piston  speed"  as  used  in  this  formula  is  not  the  actual 
speed  of  the  piston,  which  is  continually  changing  from  nothing  at  the 
centers  to  the  maximum  near  the  middle  of  the  stroke,  nor  the  number 
of  feet  passed  through  by  the  piston  per  minute,  but  the  number  of 
feet  through  which  the  pressure  acts  per  minute.  Notice  too  that  it  is 
per  minute.  If  it  were  per  second  the  divisor  would  have  to  be  550 
instead  of  33,000;  and  if  per  hour  the  divisor  would  be  1,980,000. 

The  double-acting  cylinder  being  the  usual  case,  and  the  data 
usually  given  being  the  stroke  in  inches  and  the  revolutions  per  minute, 
Table  II,  has  been  prepared  for  these  conditions.  In  a  single-acting 
steam  engine,  taking  steam  only  once  per  revolution,  or  at  every  second 
stroke,  the  "piston  speed"  of  the  formula  on  page  96  would  be  the  prod- 
uct of  the  stroke  in  inches  and  the  revolutions  per  minute  divided  by 
12,  or  one-half  the  value  given  by  the  table  for  a  double-acting  engine. 
For  a  gas  engine  this  "piston  speed"  would  be  the  stroke  in  inches  mul- 
tiplied by  the  number  of  explosions  per  minute  and  divided  by  12. 

USE  OF  THE  TABLE 

When  the  given  number  of  revolutions  can  be  found  at  the  head 
of  the  column  the  piston  speed  will  be  found  in  the  column  under  it 
opposite  the  stroke  in  inches. 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  38  inches  when  running  at  70  revolutions  per  minute? 

Follow  the  horizontal  line  opposite  38  to  the  column  under  70  and 
find  443.33  feet  per  minute,  the  value  sought. 

If  the  number  of  revolutions  is  even  hundreds  instead  of  tens,  as 
given  in  the  table,  the  values  of  the  table  should  be  multiplied  by  10, 


98  THE   STEAM   ENGINE   INDICATOR 

which  may  be  done  by  adding  a  cipher  when  the  tabular  value  is  a  whole 
number,  or  by  moving  the  decimal  point  one  point  to  the  right,  if  it 
contains  a  fraction. 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  8  inches  when  running  at  300  revolutions  per  minute? 

Opposite  8  and  under  30  find  40,  to  which  add  a  cipher,  giving  400 
feet  per  minute. 

Or  take  the  same  engine  running  400  revolutions.  Opposite  8  under 
40  find  53.33,  which  multiplied  by  10  by  moving  the  decimal  point  one 
place  to  the  right,  gives  533.3,  the  value  sought. 

If  the  number  of  revolutions  given  is  a  unit  the  tabular  value  must 
be  divided  by  10  by  cutting  off  a  cipher  or  pointing  off  one  space  if  it 
is  a  whole  number,  or  by  moving  the  decimal  point  one  place  to  the  left 
if  there  is  a  fraction.  Thus  the  piston  speed  of  an  engine  with  a  stroke 
of  138  inches  would  be,  when  running  at  9  revolutions,  207  feet,  found 
by  dropping  the  final  cipher  from  the  value  given  for  90  feet.  The 
piston  speed  of  an  engine  with  a  stroke  of  136  inches  at  8  revolutions 
would  be  181.333  feet,  found  by  moving  the  decimal  one  point  to  the 
left  in  the  tabular  value  for  80  feet. 

When  the  given  number  of  revolutions  contains  more  than  one  figure 
the  values  for  the  units,  tens,  hundreds,  etc.,  must  be  found  separately 
and  added  together. 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  72  inches  when  running  at  46  revolutions  per  minute? 

First  look  up  the  value  for  40,  then  the  value  for  6  as  directed  above. 
Their  sum  will  be  the  value  for  46 ;  thus : 

Value  for  40=480 
"          6=  72 

46=552 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  68  inches  running  at  54  revolutions  per  minute? 

Value  for  50  =566.667 
4=  45.333 

612.000  ft.  per  min. 

The  only  two  fractions  occurring  in  the  table  are  J  and  §=33333  + 
and  66666  +  .  They  can  be  carried  out  to  any  degree  of  accuracy  desired 
by  adding  additional  3's  and  6's,  making  the  last  6  a  7.  This  was  done 
in  the  above  value  for  50. 


COMPUTING   THE   HORSE-POWER  99 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  62  inches  when  running  at  126  revolutions  per  minute? 

Value  for  100-1033.33 

20=  206.67 

"  6=     62.00 


126  =  1302.00  ft.  per  min. 

If  the  number  of  revolutions  has  a  fraction,  simply  reduce  it  to  a 
decimal  and  continue  as  above,  shifting  the  decimal  point  in  the  tabular 
value  one  point  to  the  left  for  each  place  the  decimal  figure  is  to  the  right. 

EXAMPLE. — What  is  the  piston  speed  of  an  engine  having  a  stroke 
of  72  inches  at  63^  revolutions  per  minute? 

63J  =63.25. 

Value  for  60.      =720. 
3.      =  36. 
"  2    =     2.4 

.05=     0.6 

63.25  =759.0  ft.  per  min. 

A  simple  and  easily  remembered  formula  for  horse-power  is : 

PANS 


H.P. 


33000 ' 


Where  P=mean  effective  pressure, 

A  =area  of  piston  in  square  inches, 

N=  number  of  working  strokes  per  minute, 

S=  length  of  stroke  in  feet. 

RULE.  —  Multiply  together  the  mean  effective  pressure,  the  area  of  the 
piston  in  square  inches,  the  number  of  working  strokes  per  minute,  and  the 
length  of  the  stroke  in  feet  and  divide  by  33,000.  The  quotient  will  be  the 
horse-power. 

EXAMPLE.  —  What  is  the  horse-power  developed  by  a  24X48  inch 
engine  running  at  70  revolutions  per  minute  with  42  pounds  M.E.P.? 

The  pressure  P=  42         Ibs.  given 

"   area         A  =452.39  sq.in.  242X.7854 
'  '   number    N  =  140       stroke  per  min.  70  X  2 

-"stroke       S=4          feet  48  ins.  -i-  12 

PANS          42X452.39X140X4 


33000  '  33000 


100  THE   STEAM   ENGINE   INDICATOR 


THE  HORSE-POWER  CONSTANT 

In  figuring  a  number  of  diagrams  from  one  engine  running  at  a  con- 
stant speed  it  is  most  convenient  to  compute  first  the  horse-power  developed 
per  pound  of  mean  effective  pressure,  and  multiply  this  "  horse-power 
constant"  by  the  mean  effective  pressure  of  each  diagram  to  find  the 
horse-power  represented  by  that  diagram.  This  can  be  done  by  con- 
sidering the  M.E.P.  in  formula  1  as  unity,  in  which  case,  as  it  is  a  multi- 
plier, it  may  be  left  out,  and  we  get 

Area X piston  speed  ANS     „  ^  i    r  TVT  -n  r> 

33QOO  °r     33ooo=H.P.  per  pound  of  M.E.P., 

and  this  H.P.  constant  multiplied  by  M.E.P.  =H.P. 

To  FIND  THE  HORSE-POWER  CONSTANT  OR  HORSE-POWER  PER  POUND 
OF  MEAN  EFFECTIVE  PRESSURE, 

RULE. — Multiply  the  piston  area  in  square  inches  by  the  piston  speed 
in  feet  per  minute  and  divide  by  33,000,  or 

Multiply  together  the  piston  area  in  square  inches,  the  number  of  work- 
ing strokes  per  minute,  and  the  stroke  in  feet,  and  divide  the  product  by 
33,000. 

EXAMPLE. — What  is  the  horse-power  constant  of  the  above  engine? 

ANS     452.39X140X4 

—  =  7.o7by. 


33000  33000 

This  multiplied  by  the  mean  effective  pressure  will  give  the  horse- 
power thus 

7.6769X42=322.4298 
as  before. 

Table  III  gives  these  constants,  i.e.,  the  horse-power  per  pound  of 
mean  effective  pressure,  directly  when  the  piston-speed  is  in  even  hun- 
dreds of  a  single  figure.  The  values  for  thousands,  tens,  units,  or  frac- 
tional quantities  can  be  found  by  changing  the  decimal  point  as  explained 
in  connection  with  the  previous  table. 

EXAMPLE. — What  horse-power  is  being  developed  by  a  4JX 8-inch 
engine  running  at  300  revolutions  per  minute  with  40  pounds  mean 
effect  ve  pressure? 

From  Table  II  we  see  that  the  piston  speed  is  400  feet  per  minute. 

From  Table  III  we  see  that  an  engine  4  J  inches  in  diameter  will  develop 
0.2149  horse-power  per  pound  of  mean  effective  pressure  at  this  piston- 
speed.  Then, 

H.P.  =40X0.2149 -8.596. 


COMPUTING   THE   HORSE-POWER 

TABLE  II 
PISTON  SPEED   IN  FEET  PER  MINUTE 

(2  X  stroke  X  revolutions)  -T-  12  =  (stroke  X  revolutions)  -7-6. 


101 


Stroke  in 
Inches 

REVOLUTIONS  PER  MINUTE. 

10 

20 

30 

40 

50 

60 

70 

80 

90 

1 

1.67 

3.33 

5 

6.67 

8.33 

10 

11.67 

13.33 

15 

2 

3.33 

6.67 

10 

13.33 

16.67 

20 

23.33 

26.67 

30 

3 

5 

10 

15 

20 

25 

30 

35 

40 

45 

4 

6.67 

13.33 

20 

26.67 

33.33 

40 

46.67 

53.33 

60 

5 

8.33 

16.67 

25 

33.33 

41.67 

50 

58.33 

66.67 

75 

6 

10 

20.00 

30 

40 

50 

60 

70 

80 

90 

7 

11.67 

23.33 

35 

46.67 

58.33 

70 

81.67 

93.33 

105 

8 

13.33 

26.67 

40 

53.33 

66.67 

80 

93.33 

106.67 

120 

9 

15 

30 

45 

60 

75 

90 

105 

120 

135 

10 

16.67 

33.33 

50  . 

66.67 

83.33 

100 

116.67 

133.33 

150 

11 

18.33 

36.67 

55 

73.33 

91.67 

110 

128.33 

146.67 

165 

12 

20 

40 

60 

80 

100 

120 

140 

160 

180 

13 

21.67 

43.33 

65 

86.67 

108.33 

130 

151.67 

173.33 

195 

14 

23.33 

46.67 

70 

93.33 

116.67 

140 

163.33 

186.67 

210 

15 

25 

50 

75 

100 

125 

150 

175 

200 

225 

16 

26.67 

53.33 

80 

106.67 

133.33 

160 

186.67 

213.33 

240 

17 

28.33 

56.67 

85 

113.33 

141.67 

170 

198.33 

226.67 

255 

18 

30 

60 

90 

120 

150 

180 

210 

240 

270 

19 

31.67 

63.33 

95 

126.67 

158.33 

190 

221.67 

253.33 

285 

20 

33.33 

66.67 

100 

133.33 

166.67 

200 

233.33 

266.67 

300 

22 

36.67 

73.33 

110 

146.67 

183.33 

220 

256.67 

293.33 

330 

24 

40 

80 

120 

160 

200 

240 

280 

320 

360 

26 

43.33 

86.67 

130 

173.33 

216.67 

260 

303.33 

346.67 

390 

28 

46.67 

93.33 

140 

186.67 

233.33 

280 

326.67 

373.33 

420 

30 

50 

100 

150 

200 

250 

300 

350 

400 

450 

32 

53.33 

106.67 

160 

213.33 

266.67 

320 

373.33 

426.67 

480 

34 

56.67 

113.33 

170 

226.67 

283.33 

340 

396.67 

453.33 

510 

36 

60 

120 

180 

240 

300 

360 

420 

480 

540 

38 

63.33 

126.67 

190 

253.33 

316.67 

380 

443.33 

506.67 

570 

40 

66.67 

133.33 

200 

266.67 

333.33 

400 

466.67 

533.33 

600 

42 

70 

140 

210 

280 

350 

420 

490 

560 

630 

44 

73.33 

146.67 

220 

293.33 

366.67 

440 

513.33 

586.67 

660 

46 

76.67 

153.33 

230 

306.67 

383.33 

460 

536.67 

613.33 

690 

48 

80 

160 

240 

320 

400 

480 

560 

640 

720 

50 

83.33 

166.67 

250 

333.33 

416.67 

500 

583.33 

666.67 

750 

52 

86.67 

173.33 

260 

346.67 

433.33 

520 

606.67 

693.33 

780 

54 

90 

180 

276 

360 

450 

540 

630 

720 

810 

56 

93.33 

186.67 

280 

373.33 

466.67 

560 

653.33 

746.67 

840 

58 

96.67 

193.33 

290 

386.67 

483.33 

580 

676.67 

773.33 

870 

60 

100 

200 

300 

400 

500 

600 

700 

800.00 

900 

102  THE  STEAM  ENGINE   INDICATOR 

TABLE  II — Continued 

PISTON   SPEED   IN   FEET   PER   MINUTE 
(2  X  stroke  X  revolutions)  -f- 12  =  (stroke  X  revolutions)  -f-  6. 

REVOLUTIONS  PEK  MINUTE. 


Stroke  in 
Inches. 

10 

20 

| 
30 

40 

50 

^ 
60 

\ 
70 

I 
80 

90 

62 

103.33 

206.67 

310 

413.33 

516.67 

620 

723.33 

826.67 

930 

64 

106.67 

213.33 

320 

426.67 

533.33 

640 

746.67 

853.33 

960 

66 

110 

220 

330 

440 

550 

660 

770 

880 

990 

68   113.33 

226.67  | 

310 

453.33 

566.67 

680 

793.33 

906.67 

1020 

70   116.67 

233.33 

350 

466.67 

583.37 

700 

816.67 

933.33 

1050 

72 

120 

240 

360 

480 

600 

720 

840 

960 

1080 

74 

123.33 

246.67 

370 

493.33 

616.67 

740 

863.33 

986.67 

1110 

76 

126.67 

253.33 

380 

506.67 

633.33 

760 

886.67 

1013.33 

1140 

78 

130 

260 

390 

520 

650 

780 

910 

1040 

1170 

80 

133.33 

266.67 

400 

533.33 

666.67 

800 

933.33 

1066.67 

1200 

82 

136.67 

273.33 

410 

546.67 

683.33 

820 

956.67 

1093.33 

1230 

84 

140 

280 

420 

560 

700 

840 

980 

1120 

1260 

86 

143.33 

286.67 

430 

573.33 

716.67 

860 

1003.33 

1146.67 

1290 

88 

146.67 

293.33 

440 

586.67 

733.33 

880 

1026.67 

1173.33 

1320 

90 

150 

300 

450 

600 

750 

900 

1050 

1200 

1350 

92 

153.33 

306.67 

460 

613.33 

766.67 

920 

1073.33 

1226.67 

1380 

94 

156.67 

313.33 

470 

626.67 

783.33 

940 

1096.67 

1253.33 

1410 

96 

160 

320 

480 

640 

800 

960 

1120 

1280 

1440 

98 

163.33 

326.67 

490 

653.33 

816.67 

980 

1143.33 

1306.67 

1470 

100 

166.67 

333.33 

500 

666.67 

833.33 

1000 

1166.67 

1333.33 

1500 

102 

170 

340 

510 

680 

850 

1020 

1190 

1360 

1530 

104 

173.33 

346.67 

520 

693.33 

866.67 

1040 

1213.33 

1386.67 

1560 

106 

176.67 

353.33 

530 

706.67 

883.33 

1060 

1236.67 

1413.33 

1590 

108 

180 

360 

540 

720 

900 

1080 

1260 

1440 

1620 

110 

183.33 

366.67 

550 

733.33 

916.67 

1100 

1283.33 

1466.67 

1650 

112 

186.67 

373.33 

560 

746.67 

933.33 

1120 

1306.67 

1493.33 

1680 

114 

190 

380 

570 

760 

950 

1140 

1330 

1520 

1710 

116 

193.33 

386.67 

580 

773.33 

966.67 

1160 

1353.33 

1546.67 

1740 

118 

196.67 

393.33 

590 

786.67 

983.33 

1180 

1376.67 

1573.33 

1770 

120 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

122 

203.33 

406.67 

610 

813.33 

1016.67 

1220 

1423.33 

1626.67 

1830 

124 

206.67 

413.33 

620 

826.67 

1033.33 

1240 

1446.67 

1653.33 

1860 

126 

210 

420 

630 

840 

1050 

1260 

1470 

1680 

1890 

128 

213.33 

426.67 

640 

853.33 

1066.67 

12SO 

1493.33 

1706.67 

1920 

130 

216.67 

433.33 

650 

866.67 

1083.33 

1300 

1516.67 

1733.33 

1950 

132 

220 

440 

660 

880 

1100 

1320 

1540 

1760 

1980 

134 

233.33 

446.67 

670 

893.33 

1116.67 

1340 

1563.33 

1786.67 

2010 

136 

226.67 

453.33 

680 

906.67 

1133.33 

1360 

1586.67 

1813.33 

2040 

138 

230 

460 

690 

920 

1150 

1380 

1610 

1840 

2070 

140 

233.33 

466.67 

700 

933.33 

1166.67 

1400 

1633.33 

1866.67 

2100 

COMPUTING   THE   HORSE-POWER  103 

What  horse-power  would  be  developed  by  an  engine  24  inches  in 
diameter  running  at  523  feet  of  piston-speed  per  minute  at  34  pounds 
M.E.P.? 

Use  Table  III  for  the  tens  and  units,  just  as  before.  In  the  line 
opposite  24  find  the 

value  of  500=6.8544 
20=0.27417 
3=0.041126 


"      523=7.169696 

horse-power  per  pound  of  mean  effective  pressure.     Then 
H.P.  =7.1697X34  =243.77. 

When  the  piston-speed  contains  a  fraction,  its  value  can  be  found 
by  shifting  the  decimal  point,  as  in  the  previous  table,  to  the  left. 

EXAMPLE. — What    horse-power    would    be    devolped    by    a    30-inch 
engine  running  at  617.23  feet  of  piston-speed  with  a  mean  effective  pres- 
sure of  47.5  pounds? 
Opposite  30  find  the 

value  of  600       =12.852 
"     of     10  .2142 

"of      7  .14994 

"of        2   -       .004284 
"     of         .03=     .0006426 


617.23  =  13.2210666 

horse-power  per  pound  of  mean  effective  pressure.     Then 
H.P.  =47.5  =  X  13.22  =627.95. 

In  the  above  examples  the  mean  effective  pressure  given  is  assumed 
to  be  the  average  of  both  ends,  and  the  horse-power  as  calculated  is 
that  of  the  whole  engine.  If  it  is  desired  to  know  the  horse-power  of 
each  end,  they  must  be  calculated  separately,  each  with  its  own  mean 
effective  pressure,  and  the  constant  taken  at  one-half  the  piston  speed, 
or  with  the  constant  taken  at  the  full  piston-speed  and  one-half  the  mean 
effective  pressure. 

EXAMPLE. — An  engine  48X84  inches,  running  at  36.5  revolutions 
per  minute,  has  a  mean  effective  pressure  in  the  head  end  of  42.7  pounds, 
and  in  the  crank  end  of  41.3  pounds,  what  is  the  horse-powrer  of  each 
end,  and  of  the  whole  engine? 


104  THE  STEAM  ENGINE   INDICATOR 

The  "horse-power  constant/'  or  the  horse-power  per  pound  of  mean 
effective  pressure  for  each  end,  will  be  one-half  that  given  by  the  table 
for  both  ends,  or  that  given  by  the  table  for  an  engine  of  the  given  diam- 
eter at  one-half  the  piston-speed.  From  the  piston-speed  table  we 
find  that  the  piston-speed  at  36.5  revolutions  of  the  double-acting  engine 
is  511  feet  per  minute.  The  piston  speed  of  each  would  be  one-half 
of  this,  or 

511-^2=255.5  ft.  per  min. 

From  the  Table  III  we  find  that  the  horse-power  per  pound  of  mean 
effective  pressure  for  a  48-inch  engine  at  this  speed  is 

value  for  200     -10.9673 
50      =  2.74182 
5  .274182 

0.5-     .0274182 

255.5  =  14.0107202 

H.P.  Head  end  =14.01X42.7-598.227 
H.P.  Crank  end -14.01  X41.3 -578.613 

H.P.  Both  ends-  1176.84 

ALLOWING  FOR  THE  ROD 

When  a  portion  of  the  area  of  the  piston  is  cut  off  by  a  rod,  as  is  usually 
the  case  in  the  crank  end,  and  as  occurs  in  the  head  end  of  a  cylinder 
tandem  to  one  behind  it,  or  with  a  tail  rod,  it  is  essential  to  accuracy 
that  an  allowance  be  made  for  such  loss  of  area.  In  the  usual  case',  that 
of  a  cylinder  having  a  rod  only  in  the  crank  end,  the  allowance  may 
be  made  by  subtracting  from  the  horse-power  computed  as  in  the  first 
example,  the  horse-power  which  would  be  developed  by  a  single-acting 
engine  having  a  diameter  equal  to  that  of  the  piston  rod,  and  with  the 
mean  effective  pressure  acting  in  the  crank  end. 

EXAMPLE. — What  horse-power  would  be  developed  by  a  24-inch 
engine  with  a  4J  piston-rod  running  at  620  feet  piston  speed  with  46.5 
pounds  mean  effective  pressure  in  the  head  end  and  47.2  in  the  crank 
end? 

From  the  table  the  constant  for  this  engine  would  be 

value  for  600=8.2253 
20=   .27417 


' '       620  =  8.49947  horse-power 
per  pound  of  average  mean  effective  pressure. 


COMPUTING  THE  HORSE-POWER  105 

The  average  mean  effective  pressure  would  be 

46.54-47.2 

— =46.85  pounds. 

The  horse-power  uncorrected  for  the  rod  would  therefore  be 
8.49947X46.85=398.2001695  H.P. 

The  horse-power  lost  by  the  presence  of  the  rod  is  that  which  would 
be  developed  by  an  engine  4f  inches  diameter  at  310  feet  of  piston  speed 
and  at  47.2  pounds  mean  effective  pressure. 

From  the  table  we  find  the  constant  for  such  an  engine  to  be 

for  300  feet  0.1367 
"10    "    0.00456 

"  310  "   0.14126 

horse-power  per  pound  of  mean  effective  pressure. 

The  mean  effective  pressure  which  would  have  acted  upon  this  area 
is  47.2  pounds. 

The  horse-power  to  be  deducted,  therefore,  is 

0.14126X47.2=6.667472  H.P. 
Deducting  this  from  the  uncorrected  horse-power  we  have 

398.2001695 
6.667472 


391.5326975 

as  the  horse-power  corrected  for  the  rod. 

A  more  convenient  way  when  a  large  number  of  diagrams  are  to  be 
figured  up  from  the  same  engine,  as  in  making  out  daily  reports  or  com- 
puting the  results  of  a  long  test,  is  to  correct  the  constant  for  the  engine 
by  subtracting  from  it  the  constant  of  the  rod  at  half  the  piston  speed 
and  multiplying  this  corrected  constant  by  the  average  mean  effective 
pressure.  Performing  the  above  example  in  this  way, 

constant  for  cylinder  8.49947 
"rod        .14126 


corrected  constant  8.35821 


106  THE  STEAM  ENGINE   INDICATOR 

which  multiplied  by  the  average  M.E.P.  gives 

835821X46.85=391.5821385  H.P. 
by  other  method  391.5326975  H.P. 

difference  .049441 

If  the  mean  effective  pressure  were  the  same  in  both  ends  this  method 
would  be  perfectly  accurate.  The  inaccuracy  which  it  involves,  and 
which  is  the  cause  of  the  above  difference,  is  due  to  multiplying  the  rod 
constant  by  the  average  M.E.P.,  instead  of  that  in  the  crank  end. 

M.E.P.  in  crank  end  47.2 
average  M.E.P.     46.85 
difference    0.35 

0.14125X0.35=0.049441 

The  error  thus  is  seen  to  be  the  product  of  the  rod  constant  and  the 
difference  between  the  average  and  the  actual  M.E.P.  in  the  crank  end 
neither  of  which  factors  are  large  enough  in  the  ordinary  case  to  make 
the  error  of  any  considerable  magnitude. 

THROUGH  RODS  AND  TAIL  RODS 

When  the  rod  is  in  both  ends  of  the  cylinder,  as  in  the  cylinder  nearesl 
the  guides  in  a  tandem  compound,  or  in  a  cylinder  with  a  tail  rod,  anc 
the  rod  is  the  same  diameter  in  both  ends,  it  is  necessary  only  to  sub- 
tract the  constant  for  an  engine  of  a  diameter  equal  to  that  of  the  rod 
at  the  full  piston  speed  from  the  constant  for  the  diameter  of  the  cylinder 
and  multiply  by  the  average  mean  effective  pressure. 

When  there  is  a  rod  in  each  end,  but  of  different  size,  each  rod  should 
be  allowed  for  separately  by  multiplying  its  constant  at  half  piston  speed 
by  the  mean  effective  pressure  acting  in  its  own  end  of  the  cylinder, 
and  subtracting  the  products  successively  from  the  horse-power  found  by 
multiplying  the  cylinder  constant  at  full  speed  by  the  average  mean 
effective  pressure. 

In  strictness,  in  order  to  find  the  power  which  is  being  developed 
by  one  end  of  the  cylinder,  a  diagram  made  of  the  line  showing  the  for- 
ward pressure  in  the  end  which  is  being  computed,  and  the  back  pres- 
sure- or  counter-pressure  line  of  the  diagram  from  the  other  end  should 
be  used.  The  counter-pressure  line  diagram  from  the  head  end  does 
not  show  the  back  pressure  against  the  piston  when  the  head  end  was 
doing  work,  but  while  the  piston  is  being  forced  backward  by  the  steam 


COMPUTING   THE   HORSE-POWER 


107 


TABLE    III 

HORSE-POWER   PER    POUND   OF   MEAN   EFFECTIVE   PRESSURE 

(Area  X  piston  speed)  -f-  33 . 000. 


Diameter 
of 
Cylinder 
or  Rod. 
Inches. 

PISTON  SPEED  IN  FEET  PER  MINUTE. 

100 

200 

300 

400 

500    600 

700 

800 

900 

2 

.00134 

.0027 

.0043 

.0054 

.0067  !  .0030 

.0094 

.0107 

.0120 

H 

.00157  .0031 

.0047 

.0063 

.0079  i  .0091 

.0110 

.0126 

.0141 

i 

.00182  .0036 

.0055 

.0073 

.0091   .0109 

.0128 

.0146 

.0164 

« 

.00209'  .0042 

.0063 

.0084 

.0105 

.0126 

.0146 

.0167 

.0188 

i 

.00238 

.0048 

.0071 

.0095 

.0119 

.0143 

.0167 

.0190 

.0214 

i* 

.00269 

,0054 

.0081 

.0107 

.0134 

.0161 

.0188 

.0215 

.0242 

1A 

.00288 

.0058 

.0086 

.0115 

.0144 

.0173 

.0202 

.0230 

.0259 

H 

.00301 

.0060 

.0090 

.0120 

.0151 

.0181 

.0211 

.0241 

.0271 

i* 

.00336 

.0067 

.0101  • 

.0134 

.0168 

.0201 

.0235 

.0268 

.0302 

11 

.00343 

.0069 

.  0103 

.0137 

.0172 

.0206 

.0240 

.0274 

.0309 

a 

.00372 

.0074 

.0112 

.0149 

.0186 

.0223 

.0260 

.0298 

.0335 

Ift 

.00402 

.0080 

.0121 

.0161 

.0201 

.0241 

.0281 

.0322 

.0362 

iA 

.00410 

.0082 

.0123 

.0164 

.0205 

.0246 

.0287 

.0328 

.0369 

If 

.00450 

.0090 

.0135 

.0180 

.0225 

.0270 

.0315 

.0360 

.0405 

U 

.00466 

.0093 

.0140 

.0186 

.0233 

.0280 

.0326 

.0373 

.0419 

1& 

.00492 

.0098 

.0148 

.0197 

.0246 

.0295 

.0344 

.0393 

.0443 

H 

.00535 

.0107 

.0161 

.0214 

.0268 

.0321 

.0375 

.0428 

.0482 

1* 

.00581 

.0116 

.0174 

.0232 

.0291 

.0349 

.0407 

.0465 

.0523 

if 

.00609 

.0122 

.0183 

.0244 

.0305 

.0365 

.0426 

.0487 

.0548 

if 

.00628 

.0126 

.0189 

.0251 

.0314 

.0377 

.0440 

.0503 

.0566 

ift 

.00678 

.0136 

.0203 

.0271 

.0339 

.0407 

.0474 

.0542 

.0610 

1A 

.00688 

.0138 

.0206 

.0275 

.0344 

.0413 

.0482 

.0550 

.0619 

If 

.00729 

.0146 

.0219 

.0292 

.0364 

.0437 

.0510 

.0583 

.0656 

U 

.00771 

.0154 

.0231 

.0308 

.0386 

.0463 

.0540 

.0617 

.0694 

iff 

.00782 

.0156 

.0235 

.0313 

.0391 

.0469 

.0548 

.0626 

.0704 

11 

.00837 

.0167 

.0251 

.0335 

.0418 

.0502 

.0586 

.0669 

.0753 

A 

.00859 

.0172 

.0258 

.0344 

.0430 

.0515 

.0601 

.0687 

.0773 

m 

.00893 

.0179 

•  .0268 

.0357 

.0447 

.0536 

.0625 

.0715 

.0804 

2 

.00952 

.0190 

.0286 

.0381 

-0476 

.0571 

.0666 

.0762 

.0857 

2tV 

.01012 

.0202 

.0304 

.0405 

.0506 

.0607 

.0709 

.0810 

.0911 

2A 

.01050 

.0210 

.0315 

.0420 

.0525 

.0630 

.0735 

.0840 

.0945 

2i 

.01074 

.0215 

.0322 

.0430 

.0537 

.0645 

.0752 

.0860 

.0967 

2& 

.01139 

.0228 

.0342 

.0456  !  .0569 

.0683 

.0797 

.0911   .1025 

2i 

.91152 

.0230 

.0346 

.0461  ;  .0576 

.0691 

.0806 

.0921   .1036 

2* 

.01205 

.0241 

.0361 

.0482 

.0602 

.0723 

.0843 

.0964 

.1084 

2& 

.01259 

.0252 

.0378 

.0504 

.0630 

.0755 

.0881 

.1007 

.1133 

2A 

.01273 

.0255 

.0382 

.0509 

.0636 

.0764 

.0891 

.1018 

.1145 

2f 

.01342 

.0268 

.0403 

.0537 

.0671 

.0805 

.0940 

.1074 

.1208 

2! 

.01371 

.0274 

.0411 

.0548 

.0686 

.0823 

.0960 

.1097 

.1234 

2^ 

.01414 

.0283 

.0424 

.0566 

.0707 

.0848 

.0990 

.1131 

.1273 

2* 

.01487 

.0297 

.0446 

.  0595 

.0744 

.0892 

.1041 

.1190  1  .1339 

2& 

.01563 

.0313 

.0469 

.0625 

.0781 

.0938 

.1094 

.  1250   .  1407 

2| 

.01609  .0322 

.0483 

.0644 

.0805 

.0965 

.1126 

.  1287   .  1448 

2| 

.01640  .0328 

.0492 

.0656 

.0820 

.0984 

.1148 

.1312 

.1476 

2H 

.01719  .0344 

.0516 

.0688 

.0860 

.  1031 

.1203 

.1375 

.1547 

2^ 

.01735  .0347 

.0521 

.0694 

.0868 

.1041 

.1215 

.1388 

.  1562 

2! 

.01800 

.0360 

.0540 

.0720 

.0900 

.1080 

.1260 

.1440 

.1620 

2* 

.01866 

.0373 

.0560 

.0746 

.0933 

.1120 

.1306 

.  1493 

.1679 

2H 

.01883 

.0377 

.0565 

.0753 

.0941 

.1130 

.1318 

.1506 

.1694 

2* 

.01967 

.0394 

.0590 

.0787 

.0984 

.1180 

.1377 

.1574 

.1770 

2A 

.02002 

.0400 

.0601 

.0801 

.1001 

.1201 

.1401 

.1602 

.1802 

2M 

.02054!  .0411 

.0616   .0821 

.1027 

.1232 

.1438 

.1643 

.1848 

108 


THE   STEAM   ENGINE   INDICATOR 


TABLE  III — Continued 

HORSE-POWER   PER   POUND    OF  MEAN  EFFECTIVE   PRESSURE 

(Area  X  piston  speed)  -f-  33.000. 


Diameter 
of 
Cylinder 
or  Rod, 
Inches. 

PISTON  SPEED  IN  FEET  PER  MINUTE. 

100 

200 

300 

400 

500 

600 

700 

800 

900 

3 

.02142 

.0428 

.0643 

.0857 

.1071 

.1285 

.1499 

.1714 

.1928 

fcV 

.02287 

.0457 

.0686 

.0915 

.1144 

.  1372 

.1601 

.1830 

.2058 

3F 

.02324 

.0465 

.0697 

.0930 

.1162 

.1395 

.1627 

.1859 

.2092 

3| 

.02437 

.0487 

.0731 

.0975 

.1219 

.1462 

.1706 

.1950 

.2193 

31- 

.02514 

.0503 

.0754 

.1006 

.1257 

.1508 

.1760 

.2011 

.2262 

ST% 

.  02592 

.0518 

.0778 

.1037 

.  1296 

.  1555 

.  1814 

.2074 

.2333 

3f 

.02711 

.0542 

.0813 

.1084 

.1355 

.  1627 

.  1898 

.2169 

,2440 

3f 

.02751 

.0550 

.0825 

.1100 

.1376 

.1651 

.1926 

.2201 

.2476 

3* 

.02915 

.0583 

.0875 

.1166 

.1458 

.  1749 

.2041 

.2332 

.2624 

31 

.03085 

.0617 

.  0926 

.1234 

.1543 

.1851 

.2160 

.2468 

.2777 

3| 

.03128 

.0626 

.0938 

.1251 

.1564 

.1877 

.2189 

.2502 

.2815 

37 
To 

.03258 

.0652 

.0977 

.1303 

.1629 

.  1950 

.2281 

.2606 

.2932 

3| 

.03347 

.0669 

.1004 

.  1339 

.1673 

.  2008 

.2343 

.2678 

.3012 

si 

.03437 

.0687 

.1031 

.1375 

.1719 

.  2062 

.2406 

.2750 

.3093 

31 

.03574 

.0715 

.1072 

.1429 

.1787 

.2144 

.2502 

.2859 

.3216 

3& 

.03620 

.0724 

.1086 

.1448 

.1810 

.2172 

.2534 

.2896 

.  3258 

4 

.03808 

.0762 

.1142 

.1523 

.1904 

.2285 

.2666 

.3046 

.3427 

4^ 

.04001 

.0800 

.  1200 

.1600 

.2001 

.2401 

.  2801 

.3201 

.3601 

4 

.  04050 

.0810 

.1215 

.1620 

.2025 

.2430 

.2835 

.3240 

.3645 

4i 

.04198 

.0840 

.1259 

.1679 

.2099 

.2519 

.2939 

.3358 

.3778 

4} 

.04300 

.0860 

.1290 

.1720 

.2149 

.  2579 

.3009 

.3439 

.3869 

4 

.04401 

.0880 

.1320 

.1760 

.2201 

.2641 

.3081 

.3521 

.3961 

41 

.04555 

.0911 

.1367 

.1822 

.2278 

.2733 

.3189 

.3644 

.4100 

4| 

.04608 

.0922 

.1382 

.1843 

.2304 

.  2765 

.3226 

.3C86 

.4147 

-  4* 

.04819 

.0964 

.1446 

.1928 

.2410 

.2892 

.3374 

.  3856 

.4337 

4| 

.05036 

.1007 

.1511 

.2014 

.2518 

.3022 

.3525 

.4029 

.4532 

4| 

.05091 

.1018 

.1527 

.2036 

.2545 

.3055 

.3564 

.4073 

.4582 

4A 

.05257 

.1051 

.1577 

.2103 

.2629 

.3154 

.  3680 

.4206 

.4731 

4| 

.05370 

.1074 

.1612 

.2149 

.2686 

.3223 

.3760 

.4298 

.4835 

4| 

.05484 

.1097 

.1645 

.2194 

.2742 

.3290 

.3839 

.4387 

.4936 

4| 

.05656 

.1131 

.  1697 

.2262 

.2828 

.3394 

.3950 

.4525 

.5090 

4^ 

.05714 

.1143 

.1714 

.2286 

.2857 

.3428 

.4000 

.4571 

.5143 

5 

.05950 

.1190 

.1785 

.2380 

.2975 

.3570 

.4165 

.4760 

.5355 

5f 

.06251 

.1250 

.1875 

.2500 

.3126 

.3751 

.4376 

.5001 

.5626 

51 

.06560 

.1312 

.1968 

.2624 

.3280 

.3936 

.4592 

.5248 

.5904 

4 

.06876 

.1375 

.2063 

.  2750 

.3438 

.4126 

.4813 

.5501 

.6188 

5^ 

.07200 

.1440 

.2160 

.2880 

.3600 

.4320 

.  5040 

.5760 

.6479 

5| 

.07530 

.1506 

.2259 

.3012 

.3765 

.4518 

.5271 

.6024 

.6777 

51 

.07869 

.1574 

.2361 

.3148 

.3934 

.4721 

.  5508 

.6295 

.7082 

5i 

.08215 

.1643 

.2465 

.3286 

.4108 

.4929 

.5751 

.6572 

.7394 

6 

.08569 

.1714 

.  2570 

.3427 

.4284 

.5141 

.  5998 

.6854 

.7711 

61 

.09297 

.1859 

.2789 

.3719 

.4648 

.5578 

.6508 

.7438 

.8367 

6£ 

.  10055 

.2011 

.3017 

.4022 

.5028 

.6033 

.7039 

.8044 

.9050 

61 

.  10844 

.2169 

.3253 

.4338 

.5422 

.6506 

.7591 

.8675 

.9760 

.11662 

.2332 

.3499 

.4665 

.5831 

.  6997 

.8163 

.9330 

.0496 

71 

.12510 

.2502 

.3753 

.5004 

.6255 

.7506 

.8757 

.0008 

.  1259 

.  13388 

.2678 

.4016 

.5355 

.6694 

.8033 

.9371 

.0710 

.2049 

7f 

.  14295 

.2859 

.4288 

.5718 

.7147 

.8577 

1  .  0006 

.1436 

.2865 

8 

.  15232 

.3046 

.4570 

.6093 

.7616 

.9139  1.0662 

.2185 

.3709 

8i 

.16199 

.3240. 

.4860 

.6480 

.8099 

.9719  1.1339 

.2959 

.4579 

8^ 

.17195 

.3439 

.5159 

.6878 

.8598 

1.0317  1.2037 

.3756 

.5476 

81 

.  18222 

.3644 

.  5467 

.7289 

.9111 

1.0933  1.2755 

.4577 

1  .  6400 

COMPUTING   THE   HORSE-POWER 


109 


TABLE  III — Continued 

HORSE-POWER   PER   POUND   OF   MEAN   EFFECTIVE   PRESSURE 

(AreaXj>iston  speed)  -h  33,000. 


Diameter 
of 
Cylinder, 
or  Rod. 
Inches. 

PISTON  SPEED  IN  FEET  PER  MINUTE. 

100 

200 

300 

400 

500 

600 

700 

i 
800          900 

9 

.  19278 

.3856 

.5783 

.7711 

.9639 

1.1567    1.3495 

1.5422 

1.7350 

9} 

.20364 

.4073 

.6109 

.8146 

1.0182 

1.2218 

1.4255 

1.6201 

1.8328 

9* 

.21479 

.4296 

.6444 

.8592    1.0740 

1.2888 

1  .  5036 

1.7184 

1.9331 

9| 

.22625 

.4525 

.6788 

.9050 

.1313 

1.3575 

1  .  5837 

1.8100 

2  .  0362 

10 

.23800 

.4760 

.7140 

.9520 

.1900 

1.4280:   1.6660 

1.9040 

2.1420 

1<H 

.25005 

.5001)      .7502 

.0002 

.2503 

1.5003    1.7504 

2.0004 

2.2505 

10* 

.26239 

.5248 

.7872 

.0496 

.3120 

1  .  5744    1  .  8368 

2.0992 

2.3615 

lOf 

.27504 

.5501 

.8251 

.  1002 

.3752 

1.6502    1.9253 

2.2003 

2.4754 

11 

.28798 

.5759 

.8639 

.1519 

.4399 

1  .  7279 

2.0159 

2  .  3038 

2.5918 

Hi 

.30122 

.6024 

.9037 

.2049 

.5061 

1.8073 

2.1085 

2.4098 

2.7110 

Hi 

.31476 

.6295 

.9443 

.2590 

.5738 

1.8885 

2.2033 

2.5181 

2.8328 

11| 

.32858 

.6572 

.9857 

.3143 

.6429 

1.9715 

2.3001 

2.6286 

2.9572 

12 

.34273 

.6855 

1.0282 

.3709 

.7136 

2.0564 

2.3991 

2.7418 

3.0845 

12£ 

.37188 

.7438 

.1156 

.4875 

1.8594 

2.2313 

2.6032 

2.9750 

3.3469 

13 

.40221 

.8044 

.2066 

.6088 

2.0111 

2.4133 

2.8155 

3.2177 

3.6199 

13* 

.43376 

.8675 

.3013 

.  7350 

2.1688 

2.6026 

3.0363 

3.4701 

3.9038 

14 

.46648 

.9330 

.3995 

1.8659 

2  .  3324 

2.7989 

3.2654 

3.7319 

4  .  1984 

14* 

.  50039 

.0008 

.5012 

2.0016 

2.5020 

3.0023 

3.5027 

4.0031 

4  .  5035 

15" 

.53548 

.0710 

.  6065 

2.1419 

2.6774 

3.2129 

3.7484 

4.2839 

4.8194 

16 

.60927 

.2185 

.8278 

2.4371 

3.0464 

3.6556 

4.2649 

4.8742 

5.4835 

17 

.68782 

.3756 

2.0635 

2.7513 

3.4391 

4  .  1269 

4.8147 

5.5025 

6.1904 

18 

.77112 

.5422 

2.3134 

3.0845 

3.8556 

4.6267 

5.3978 

6  .  1690 

6.9401 

19 

.85918 

.7184 

2.5775 

3.4367 

4.2959 

5.1551 

6.0143 

6.8735 

7.7326 

20 

.95200 

.9040 

2.8560 

3.8080 

4.7600 

5.7120 

6.6640 

7.6160 

8.5680 

21 

1.04957 

2.0991 

3.1487 

4  .  1983 

5.2479 

6.2975 

7.3470 

8.3966 

9.4462 

22 

.15191 

2.3038 

3  .  4557 

4.6076 

5.7595 

6.9115 

8.0634 

9.2153 

10.3672 

23 

.25903 

2.5181 

3.7771 

5.0361 

6.2952 

7.5542 

8.8132 

10.0722 

11.3313 

24 

.37087 

2.7417^  4.1126 

5.4835 

6.8544 

8.2253 

9  .  5962 

10.9670 

12.3379 

25 

.48748 

2.9750J  4.4625 

5.9499 

7.4374 

8.9249 

10.4124 

11.8999 

13  .  3874 

26 

.60887 

3.2177 

4.8266 

6.4355 

8.0444 

9.6533 

11.2622 

12.8710  14.4799 

27 

.73503 

3.4701 

5.2051 

6.9401 

8.6752 

10.4102 

12.1452 

13.8802  15.6153 

28 

.86591 

3.7318 

5.5977 

7.4636 

9.3295 

11.195513.0614 

14.9273 

16.7932 

29 

2.00157 

4.0031 

6.0047 

8.006310.0079 

12.009514.0110 

16.0126  18.0142 

30 

2.15988 

4.3198 

6.4796 

8.6395110.7994 

12.9593 

15.1192 

17.2790  19.4389 

31 

2.28718 

4.5744 

6.8615 

9.1487  11.4359 

13.7231 

16.0103 

18.2975 

20.5846 

32 

2.43712 

4.8742 

7.3114 

9.748512.1856 

14.6227 

17.0598 

19.4970 

21.9341 

33 

2.59182 

5.1836 

7.7755 

10.367312.9591 

15.5509  18.1427 

20.7345 

23.3264 

34 

2.75127 

5.5025    8.2538 

11.0051  13.7564 

16.5076  19.2589 

22.0102 

24.7615 

35 

2.91548 

5.8310 

8.7465111.661914.5774 

17.492920.4084 

23.3239 

26.2394 

36 

3.08455 

6.1691 

9.  2535i  12.  3379  15.  4224 

18.506921.5914 

24.6759 

27.7604 

37 

3.25818 

6.5164 

,  9.774613.032816.2911 

19.549322.8075 

26  .  0657 

29.3239 

38 

3.43667 

6.8733 

10.3101  13.  7468J  17.  1835 

20.6202124.0569 

27.4936 

30.9303 

39 

3.62000 

7.2400 

10.860014.480018.1000 

21.720025.340028.960032.5800 

40 

3.80788 

7.6158 

11.423615.231519.0394 

22.8473 

26.6552 

30.463034.2709 

41 

4.00091 

8.0018 

12.0027  16.0036:20.0046 

24.0055 

28.006432.0073 

36.0082 

42 

4.19818 

8.3964 

12.  5945!  16.  7927;20.  9909 

25.1991 

29.387333.5854 

37.7836 

43 

4.40061 

8.8012 

13.201817.602422.0030 

26.4036 

30.804235.2048 

39.6055 

44 

4.60758 

9.2152 

13.8227!18.430323.0379 

27.6455 

32.253136.8606 

41.4682 

45 

4.81939    9.6388 

•14.  4582;  19.  2776  24.  0970 

28.9163 

33.735738.5551 

43.3745 

46 

5.0360610.0721 

1  15.  1082  21.  1442  25.  1803 

30.2164 

35.2524140.2885  45.3245 

47 

5.25727 

10.5145 

15.  7718  21.  0291  :26.  2863  31.  5436 

36.800842.0582 

47.3154 

48 

5.48364 

10.9673 

16.450921.934627.4182132.9018 

38.3815 

43.8691 

49.3528 

110  THE   STEAM   ENGINE   INDICATOR 

TABLE  III — Continued 

HORSE-POWER  PER  POUND   OF  MEAN  EFFECTIVE   PRESSURE 

(AreaX piston  speeds 33, 000.) 


M  I  72 

££ 

-,••3 
C  O 

.Stf 

»8 

PISTON  SPEED  IN  FEET  PER  MINUTE. 

100 

200 

300 

400 

500 

600 

700 

800 

900 

49 

5.71424 

11.4285 

17.1427 

22.8570 

28.5712 

34  .  2854 

39.9997 

45.7139 

51.4282 

50 

5.95000 

11.9000 

17.8500 

23.8000 

29.7500 

35.7000 

41.6500 

47.6000 

53  .  550C 

51 

6.19030 

12.3806 

18.5709 

24.7612 

30.9515 

37.1418 

43.3321 

49  .  5224 

55.7127 

52 

6.43545 

12  .  8709 

19.3604 

25.7418 

32  .  1773 

38.6127 

45  .  0482 

51.4836 

57.9191 

53 

6  .  68535 

13.3707 

20.0561 

26.7414 

33.4268 

40.1121 

46  .  7975 

53.4828 

60.1682 

54 

6.94000 

13.8800 

20.8200 

27.7600 

34  .  7000 

41.6400 

48  .  5800 

55  .  5200 

62.460C 

55 

7  .  19939 

14.3988 

21.5982 

28.7976 

35.9970 

43  .  1963 

50.3957 

57.5951 

64.7945 

56 

7.46364 

14.9273 

22.3910 

29.8547 

37.3183 

44.7820 

52.2457 

59.7093 

67.173C 

57 

7.73273 

15.4655 

23.1982 

30.9309 

38.6637 

46  .  3964 

54.1291 

61.8618 

69  .  5946 

58 

8.00636 

16.0127 

24.0191 

32.0254 

40.0318 

48  .  0382 

56.0445 

64  .  0509 

72.0572 

59 

8.28485 

16.5697 

24  .  8546 

33  .  1394 

41.4243 

49.7091 

57.9940 

66.2788 

74.5637 

60 

8.56788 

17.1358 

25.7036 

34.2715 

42.8394 

51.4073 

59.9752 

68.5430 

77.1109 

61 

8.85606 

17.7121 

26  .  5682 

35.4243 

44.2803 

53  .  1364 

61.9924 

70.8485 

79  .  7045 

62 

9  .  14879 

18.2976 

27.4464 

36  .  5952 

45.7440 

54.8927 

64.0415 

73.1903 

82.3391 

63 

9.48364 

18.9673 

28.4509 

37.9346 

47.4182 

56.9018 

66  .  3855 

75.8691 

85.3528 

64 

9.74848 

19.4970 

29.2454 

38.9939 

48.7424 

58.4909 

68.2394 

77.9878 

87  .  7363 

65 

10.05545 

20.1109 

30.1664 

40.2218 

50.2773 

60.3327 

70.3882 

80.4436 

90.4991 

66 

10.36727 

20.7345 

31.1017 

41.4690 

51.8362 

62.2035 

72.5707 

82.9379 

93  .  3052 

67 

10.68394 

21.3679 

32.0518 

42.7358 

53.4197 

64  .  1036 

74.7876 

85.4715 

96.1545 

68 

11.00515 

22.0103 

33  .  0155 

44.0206 

55.0258 

66  .  0309 

77.0361 

88.0412 

99  .  0464 

69 

11.33121 

22.6624 

33.9936 

45  .  3248 

56.6561 

67.9873 

79.3185 

90.6497 

101.9809 

70 

11.66212 

23  .  3242 

34  .  9864 

46.6485 

58.3106 

69.9727 

81.6348 

93.2970 

104.9591 

71 

11.99758 

23.9952 

35.9927 

47.9903 

59.9879 

71.9855 

83.9831 

95.9806 

107.9782 

72 

12.33788 

24.6758 

37.0136 

49.3515 

61.6894 

74.0273 

86.3651 

98.7030 

111.0409 

73 

12.68303 

25.3661 

38.0491 

50.7321 

63.4152 

76.0982 

88.7812 

101.4642 

114.1473 

74 

13.03273 

26.0655 

39.0982 

52  .  1309 

65.1637 

78.1964 

91.2291 

104.2618 

117.2946 

75 

13.38758 

26.7752 

40.1627 

53  .  5503 

66.9379 

80.3255 

93.7131 

107.1006 

120.4882 

76 

13.74697 

27.4939 

41.2409 

54.9879 

68.7349 

82.4818 

96.2288 

109.9758 

123.7227 

77 

14.11091 

28.2218 

42.3327 

56.4436 

70.5546 

84.6655 

98  .  7764 

112.8873 

126.9982 

78 

14.48000 

28.9600 

43.4400 

57.9200 

72.4000 

86  .  8800 

101.3600 

115.8400 

130.3200 

79 

14.85364 

29.7073 

44  .  5609 

59.4146 

74.2682 

89.1218 

103.9755 

118.8291 

133.6828 

80 

15.23182 

30.4636 

45.6955 

60.9273 

76.1591 

91.3909 

106.6227 

121.8546 

137.0864 

81 

15.61515 

31.2303 

46.8455 

62.4606 

78.0758 

93.6909 

109.3061 

124.9212 

140.5364 

82 

16.00303 

32.0061 

48.0091 

64.0121 

80.0152 

96.0182 

112.0212 

128.0242 

144.0273 

83 

16.39576 

32.7915 

49.1873 

65.5830 

81.9788 

98.3746 

114.7703 

131.1661 

147.5618 

84 

16.79333 

33  .  5867 

50.3800 

67.1733 

83.9667 

100.7600 

117.5533 

134.3466 

151.  HOC 

85 

17  .  19545 

34.3909 

51  .  5864 

68.7818 

85.9773 

103.1727 

120.3682 

137  .  5636 

154.7591 

86 

17.60242 

35.2048 

52.8073 

70.4097 

88.0121 

105.6145 

123.2170 

140.8194 

158.4218 

87 

18.01424 

36  .  0285 

54.0427 

72.0570 

90.0712 

108.0854 

126.0997 

144.1139 

162.1282 

88 

18.43061 

36.8612 

55.2918 

73.7224 

92.1531 

110.5837 

129.0143 

147.4449 

165.8755 

89 

18.85182 

37  .  7036 

56.5555 

75.4073 

94.2591  113.1109 

131.9627 

150.8146 

169.6664 

90 

19.27788 

38.5558 

57.8336 

77.1115 

96  .  3894 

115.6673 

134.9452 

154.2230 

173.5001 

91 

19  .  70879 

39.4176 

59.1264 

78.8352 

98  .  5440 

118.2527 

137.9615 

157.6703 

177.3791 

92 

20.14424 

40.2885 

60.4328 

80.5771 

100.7214 

120.8656 

141.0099 

161.1542 

181.2985 

93 

20.58455 

41.1691 

61.7537 

82  .  3382 

102.9228 

123  .  5073 

144.0919 

164.6764 

185.261C 

94 

21.02970 

42.0594 

63.0891 

84.1188 

105.1485126.1782 

147.2079 

168.2376 

189  .  2673 

95 

21.47940 

42.9588 

64.4382 

85.9176 

107.3970 

128.8764 

150.3558 

171.8352 

193.3146 

96 

21.93394 

43.8679 

65.8018 

87.7358 

109.6697 

131.6036 

153.5376 

175.4715197.4055 

97 

22.39333 

44  .  7867 

67.1801 

89.5735 

111.9668 

134  .  3642 

156.7535 

179.  14691201.  5403 

98 

22.85758 

45.7152 

68.5727 

91.4303 

114.2879 

137.1455 

160.0031 

182.8606205.7182 

99 

23  .  32626 

46.6525 

69.9788 

93.3050 

116.6313 

139.9576 

163.2838 

186.6101209.9363 

100 

23.80000 

47.6000 

71.4000 

95.2000 

119.0000 

142.8000 

166.6000 

190.4000214.200C 

COMPUTING   THE   HORSE-POWER 


111 


in  the  crank-end.  The  effective  pressure  at  an}'  time  in  the  forward 
stroke  is  the  pressure  in  the  head-end  at  that  instant  minus  the  pressure 
in  the  crank-end,  and  to  get  the  proper  mean  effective  pressure  during 
the  forward  stroke  we  should  take  the  mean  pressure  on  the  head-end 
less  the  mean  back  pressure  on  the  crank-end.  This  would  make  no 
difference  in  the  computed  power  of  the  engine  as  a  whole,  for  what  was 
lost  on  one  end  would  be  gained  by  the  other,  but  it  would,  if  the  back- 
pressure lines  were  different,  affect  the  amounts  of  power  indicated 
at  the  different  ends,  and  comes  into  the  question  of  balancing  the  load 
equally.  In  New  England  factories  it  is  common  to  run  an  engine  one- 
half  condensing,  that  is,  to  have  a  separate  exhaust  pipe  for  each  end, 
one  running  to  the  condenser  and  the  other  end  exhausting,  perhaps 


FIG.  100. 

under  a  back  pressure  for  heating,  etc.  The  diagrams  from  such  an  engine 
would  be  like  Fig.  100.  Obviously  the  load  would  not  be  equally  divided 
between  the  two  ends  of  the  cylinder  when  the  areas  of  the  diagrams 
were  equal.  When  the  piston  is  on  the  line  A B  and  moving  in  the  direc- 
tion of  the  arrow  there  is  a  pressure  urging  it  forward  proportional  to 
the  height  of  A  and  the  back  pressure  is  proportional  only  to  the  height 
of  B,  so  that  the  effective  pressure  is  A  B,  although  if  we  take  the  back- 
pressure line  of  the  head-end  diagram  it  will  appear  to  be  only  AC.  The 
diagram  from  the  crank-end  would  appear,  taken  by  itself,  to  have  an 
effective  pressure  proportional  to  EF  when  the  piston  was  at  that  point 
in  the  stroke,  but  since  the  piston  is  moving  against  a  back  pressure 
proportional  to  the  height  of  D  the  effective  pressure  at  that  point  is 
DE.  The  effort  of  both  ends  upon  the  crank  pin  cannot  be  balanced  by 
making  the  area  of  the  crank-end  diagram  equal  to  that  of  the  head-end. 


112 


THE   STEAM   ENGINE   INDICATOR 


The  work  actually  done  upon  the  crank  when  the  piston  is  moving  for- 
ward is  found  by  combining  the    back-pressure  line  of  the  crank-end 


FIG.  101. 


diagram  with  the  forward-pressure  line  of  the  head-end  diagram  as  in 
Fig.  101,  and  vice  versa  for  the  backward  strokes  as  in  Fig.   102.     The 


FIG.  102. 


work  will  be  equalized  between  the  two  ends  when  the  area  of  these 
reconstructed  diagrams  are  equal,  proper  allowance  being  made  for  the 
piston  rod. 


CHAPTER   XIV 

MEAN  EFFECTIVE  PRESSURE  AND  POINT  OF  CUT-OFF 
BY  COMPUTATION 


THE  mean  effective  pressure  of  steam  working  between  given  limits 
of  pressure  and  with  a  given  ratio  of  expansion  may  be  calculated 
upon  the  assumption  that  the  product  of  its  volume  and  pressure  remains 
constant  (see  chapter  on  expansion),  and  such  calculation  is  of  use  in 
designing,  selecting  or  estimating  the  horse-power  of  an  engine. 

In  Fig.  103  let  vertical  distances  represent  pressures,  and  horizontal 
distances  volume,  as  in  the  ordinary  indicator  diagram.  Let  OX  be  the 


Aa 


^ 

1 


: 


0  0 


2 
FIG.  103. 


line  of  absolute  zero  of  pressure  and  OA  the  zero  of  volume.  If  we 
start  with  the  volume  AB  of  steam  of  a  pressure  OA  and  expand  it  in  the 
usual  unjacketed  cylinder  through  the  usual  range,  the  expansion  line 
will  follow  more  or  less  closely  the  curve  BC,  which  passes  through 
points  so  located  that  the  product  of  the  pressure  and  volume  is  constant. 
For  instance,  if  the  volume  is  doubled,  the  pressure  will  be  halved,  and 
the  line  will  pass  through  6,  which  is  twice  as  far  from  the  line  of  zero 
volume,  but  only  one-half  as  far  above  the  line  of  zero  pressure  as  the 
point  B. 

113 


114  THE   STEAM  ENGINE   INDICATOR 

Suppose  AB  to  be  the  steam  line,  and  BC  the  expansion  line  of  a 
diagram  from  a  steam  engine  cylinder.  The  average  height  of  the  dia- 
gram would  be  the  average  forward  pressure  during  the  stroke  on  the 
scale  to  which  it  is  drawn.  Since  the  area  is  the  average  height  multi- 
plied by  the  length,  the  area  divided  by  the  length  is  the  average  height, 
which  represents  the  average  pressure. 

It  is  easy  to  see  that  with  the  expansion  curve  following  the  definite 
law  the  area  BCX1  will  be  a  definite  proportion  of  the  area  A  BIO 
for  any  particular  ratio  of  expansion.  For  four  expansions,  for  example, 
i.e.,  when  the  final  volume  is  four  times  the  initial  volume,  which  is 
what  is  meant  by  a  "ratio  of  expansion"  of  four,  the  area  under  the 
expansion  line  is  1.3863  times  that  under  the  steam  line  to  whatever 
scale  the  diagram  is  drawn.  Table  IV  at  the  end  of  the  volume  gives 
the  proportion  between  these  two  areas  for  other  ratios  of  expansion 
under  the  title  of  "  Hyperbolic  Logarithms." 

If  we  make  OA  equal  one  pound  pressure  and  01  one  unit  of  volume, 
then  the  area  ABIO  will  be  1X1=1,  and  the  area  BCXl  will  be  1.3863 
(for  four  expansions).  The  total  area  then  in  these  units  will  be  2.3863, 
and  the  length  in  the  same  units  4,  so  that  the  average  height  on  the 
scale  selected  for  the  expression  of  one  pound  would  be  2.3863  divided 
by  4,  and  this  would  be  the  average  or  mean  forward  pressure. 

To  FIND  THE  MEAN  FORWARD  PRESSURE  PER  POUND  OF 

INITIAL 

RULE. — Divide  1  plus  the  hyperbolic  logarithm  of  the  ratio  of  the  ex- 
pansion by  that  ratio;  the  quotient  will  be  the  mean  forward  pressure  per 
pound  of  initial. 

The  logarithms  will  be  found  in  Table  IV  at  the  end  of  the  volume. 

The  column  headed  0%  in  Table  V  was  calculated  in  this  way,  and 
gives  the  mean  forward  pressure  per  pound  of  absolute  initial  pressure, 
expanded  in  a  cylinder  without  clearance.  When  the  piston  does  not 
pass  through  the  full  length  of  the  cylinder,  or  more  properly  does  not 
displace  the  full  volume  of  the  expanding  steam,  we  would  have  the 
volume  AB  expanding  into  the  volume  OX,  while  the  piston  moves 
only  through  the  distance  oX  and  is  displaced  only  through  the  volume 
aB  by  the  entering  steam.  In  order  to  take  care  of  the  clearance,  the 
formula  becomes  that  printed  above  the  table,  and  with  this  formula 
the  remaining  columns  of  the  table  are  calculated.  By  its  use  the  mean 
forward  pressure  of  the  ideal  diagram  may  be  easily  calculated  for  any 
initial  pressure,  ratio  of  expansion  and  clearance. 

EXAMPLE. — What  would  be  the  mean  effective  pressure  in  an  engine 
having  3  per  cent  clearance,  with  an  initial  pressure  of  90  pounds  gage, 


MEAN   EFFECTIVE   PRESSURE   AND   POINT   OF   CUT-OFF          115 

TABLE  V 

MEAN   PRESSURE   PER   POUND   OF   INITIAL,   WITH    DIFFERENT 
CLEARANCES   AND   POINTS   OF   CUT-OFF 


Fraction  of 
Stroke 
Complete  at 
Cut-off. 

PERCENTAGE  OF  CLEARANCE 

0% 

1% 

1.5% 

2% 

2.5% 

3% 

3.5% 

4% 

4.5% 

5% 

5.5% 

6% 

v,o 

.1 

3303 

3439 

3505 

3568 

.3630 

.3690 

.3750 

.3808 

.3864 

.3919 

.3974 

.4027 

l/9 

.111 

3549 

3677 

3738 

3798 

.3856 

.3913 

.3968 

.4022 

.4075 

.4129 

.4178 

.4227 

*/• 

.125 

3849 

3966 

4023 

4078 

.4132 

.4187 

.4237 

.4287 

.4338 

.4386 

.4433 

.4480 

y, 

.143 

4213 

4320 

.4370 

4420 

.4471 

.4518 

.4565 

.4612 

.4655 

.4699 

.4743 

.4788 

.15 

4346 

4447 

4497 

4546 

.4794 

.4639 

.4684 

.4729 

.4774 

.4816 

.4860 

.4901 

Ye 

.167 

4662 

4757 

4802 

4844 

.4890 

.4933 

.4973 

.5014 

.5056 

.5096 

.5134 

.5173 

3Ae 

.188 

5013 

5097 

5138 

5181 

.  5217 

.5259 

.5295 

.5332 

.5367 

.5405 

.5440 

.5474 

'/• 

.20 

5219 

5298 

5336 

5376 

.5414 

.5449 

.5482 

.5517 

.5556 

.5588 

.5623 

.5656 

.21 

5376 

5453 

5489 

5523 

.5560 

.5595 

.5628 

.5664 

.5698 

.5730 

.5760 

.5795 

.22 

5533 

5602 

5639 

5673 

.5704 

.5740 

.5773 

.5804 

.5834 

.5868 

.5900 

.5931 

.23 

5681 

5750 

5781 

5815 

.5848 

.5878 

.5913 

.5940 

.5971 

.6001 

.6029 

.6063 

.24 

5827 

5891 

5922 

5952 

.5986 

.6012 

.6042 

.6071 

.6106 

.6131 

.6162 

.6184 

'A 

.25 

5966 

6025 

6059 

6090 

.6120 

.6148 

.6174 

.6207 

.6229 

.6258 

.6286 

.6312 

.26 

6105 

6162 

6190 

6218 

.6251 

.6274 

.6304 

.6332 

.6359 

.6385 

.6408 

.6430 

.27 

6232 

6294 

6319 

6350 

.6370 

.6398 

.6424 

.6448 

.6480 

.6501 

.6531 

.6549 

.28 

6363 

6416 

.6445 

6471 

.6496 

.6520 

.6551 

.6572 

.6600 

.6618 

.6644 

.6669 

.29 

6491 

6545 

.6569 

6592 

.6613 

.6642 

.6660 

.6686 

.6712 

.6736 

.6759 

.6780 

3AO 

.30 

6609 

6663 

.6684 

.6712 

.6729 

.6755 

.6779 

.6803 

.6825 

.6845 

.6864 

.6882 

Vie 

.313 

6760 

6805 

.6830 

.6855 

.6878 

.6899 

.6919 

.6938 

.6956 

.6985 

.7000 

.7026 

.32 

6851 

6891 

.6914 

.6935 

.6956 

.6974 

.7004 

.7021 

.7035 

.7062 

.7074 

.7099 

Vs 

.333 

6988 

.7029 

.7047 

.7076 

.7092 

.7106 

.7132 

.7144 

.7168 

.7190 

.7212 

.7219 

.34 

7067 

.7115 

.7130 

.7145 

.7171 

.7183 

.7207 

.7230 

.7238 

.7259 

.7279 

.7298 

.35 

.7178 

.7220 

.7232 

.7256 

.7266 

.7288 

.7310 

.7330 

.7350 

.7368 

.7370 

.7402 

.36 

.7281 

.  7316 

.7338 

.7346 

.7367 

.7386 

.7405 

.7422 

.7439 

.7454 

.7468 

.7482 

y« 

.375 

.7433 

.7458 

.7476 

.7494 

.7510 

.7525 

.7539 

.7569 

.7582 

.7593 

.7603 

.7630 

.38 

.7475 

.7512 

.7528 

.7544 

.7559 

.7573 

.7586 

.7615 

.7626 

.7636 

.7662 

.7670 

.39 

.7566 

.7613 

.7627 

.7640 

.7653 

.7664 

.7691 

.7700 

.7708 

.7734 

.7740 

.7764 

Vs 

.40 

.7665 

.7691 

.7719 

.7729 

.7738 

.7765 

.7772 

.7778 

.7802 

.7806 

.7829 

.7831 

7/ 
/16 

.438 

.8000 

.8024 

.8030 

.8044 

.8063 

.8068 

.8079 

.8096 

.8104 

.8115 

.8127 

.8138 

.45 

.8089 

.8127 

.8130 

.8141 

.8158 

.8165 

.8176 

.8187 

.8199 

.8210 

.8221 

.8231 

Vi 

.50 

.8466 

.8484 

.8492 

.8503 

.8513 

.8522 

.8530 

.8539 

.8548 

.8556 

.8565 

.8573 

.55 

.8733 

.8792 

.8810 

.8817 

.8824 

.8831 

.8838 

.8844 

.8851 

.8858 

.8864 

.8871 

%6 

.563 

.8868 

.8875 

.8882 

.8888 

.8895 

.8901 

.8908 

.8914 

.8920 

.8926 

.8932 

.8938 

3/5 

.60 

.9064 

.9076 

.9081 

.9087 

.9092 

.9097 

.9102 

.9107 

.9112 

.9117 

.9122 

.9127 

V, 

.625 

.9188 

.9194 

.9201 

.9206 

.9210 

.9215 

.9220 

.9224 

.9228 

.9233 

.9237 

.9241 

.65 

.9300 

.  9308 

.9312 

.  9316 

.9320 

.9323 

.9327 

.9331 

.9335 

.9338 

.9342 

.9340 

V3 

.667 

.9371 

.9378 

.9382 

.9385 

.9389 

.9392 

.9396 

.9399 

.9402 

.9405 

.9408 

.9411 

U/ie 

.688 

.9451 

.9457 

.9460 

.9463 

.9466 

.9469 

.9472 

.9475 

.9478 

.9480 

.9483!.  9486 

7Ao 

.70 

.9497 

.9502 

.9505 

.9508 

.9511 

.9513 

.9516 

.9518 

.9521 

.9524 

.9526 

.9528 

3A 

.75 

.9657 

.9661 

.9663 

.9665 

9667 

.9668 

.9670 

.9672 

.9674 

.9675 

.9677 

.9679 

116  THE   STEAM  ENGINE   INDICATOR 

TABLE    V — Continued 

MEAN   PRESSURE   PER   POUND   OF   INITIAL,    WITH   DIFFERENT 
CLEARANCES   AND   POINTS   OF   CUT-OFF 


PERCENTAGE  OF  CLEARANCE 

Fraction  of 
Stroke 
Complete  at 
Cut-off. 

6.5% 

7% 

7.5% 

8% 

8.5% 

9% 

9-5% 

10% 
.4409 

10.5% 

11% 

11.5% 

12% 

.4076 

.4126 

.4176 

.4225 

.4271 

.4320 

.4366 

.4453 

.4498 

.4540 

.4580 

Vio 

.1 

.4278 

.4326 

.4373 

.4417 

.4462 

.4507 

.4549 

.4593 

.4633 

.4676 

.4715 

.4757 

'/• 

.11 

.4527 

.4571 

.4615 

.4657 

.4700 

.4740 

.4782 

.4821 

.4858 

.4897 

.4938 

.4973 

Vs 

.12 

.4827 

.4871 

.4908 

.4951 

.4987 

.5026 

.5062 

.5101 

.5138 

.5173 

.5205 

.5242 

1A 

.14 

.4939 

.4978 

.5020 

.5059 

.5096 

.5131 

.5169 

.5204 

.5237 

.5274 

.5309 

.5342 

.15 

.5210 

.5245 

.5283 

.5318 

.5352 

.5389 

.5417 

.  5457 

.5488 

.5517 

.5551 

.5583 

Ye 

.16 

.5511 

.5546 

.5579 

.5610 

.5639 

.5673 

.5705 

.5736 

.5764 

.5791 

.5825 

.5848 

Vi, 

.18 

.5687 

.5716 

.5750 

.5782 

.5812 

.5841 

.5868 

.5901 

.5924 

.5954 

.5982 

.6009 

y« 

.20 

.5821 

.5853 

.5882 

.5910 

.5944 

.5968 

.5998 

.6028 

.6055 

.6081 

.6106 

.6129 

.21 

.5959 

.5986 

.6011 

.6043 

.6073 

.6101 

.6128 

.6154 

.6177 

.6199 

.6230 

.6249 

.22 

.6087 

.6118 

.6138 

.6166 

.6192 

.6225 

.6248 

.6270 

.6300 

.6318 

.6345 

.6371 

.23 

.6212 

.6239 

.6264 

.6297 

.6319 

.6340 

.6369 

.6397 

.6413 

.6438 

.6462 

.6485 

.24 

.6336 

.6359 

.6390 

.6410 

.6438 

.6465 

.6480 

.6505 

.6528 

.  6550 

.6570 

.6602 

y< 

.25 

.6460 

.6479 

.6507 

.6533 

.6548 

.6571 

.6594 

.6626 

.6646 

.6665 

.6682 

.6711 

.26 

.6576 

.6601 

.6626 

.6649 

.6670 

.6691 

.6710 

.6728 

.6757 

.6772 

.6799 

.6812 

.27 

.6692 

.6714 

.6735 

.6755 

.6773 

.6803 

.6818 

.6833 

.6859 

.6885 

.6895 

.6918 

.28 

.6800 

.6819 

.6849 

.6865 

.6880 

.6906 

.6919 

.  6943 

.  6967 

.6990 

.6997 

.7018 

.29 

.6911 

.6927 

.6954 

.6966 

.6991 

.7002 

.7024 

.7046 

.7067 

.7087 

.7107 

.7125 

Vio 

.30 

.7039 

.7063 

.7073 

.7096 

.7117 

.7138 

.7157 

.7176 

.7194 

.7211 

.7226 

.7241 

5/lti 

.31 

.7123 

.7131 

.715$ 

.7173 

.7193 

.7211 

.7229 

.7245 

.7261 

.7275 

.7289 

.7319 

.32 

.7239 

.7257 

.7275 

.7292 

.7308 

.7323 

.7353 

.7366 

.7378 

.7389 

.7417 

.7426 

Vs 

.33 

.7316 

.7333 

.  7349 

.7364 

.7378 

.7391 

.7421 

.7432 

.7442 

.7469 

.7477 

.7484 

.34 

.7417 

.7432 

.7445 

.7457 

.7468 

.7496 

.7506 

.7514 

.7540 

.7546 

.7571 

.7575 

.35 

.7511 

.7523 

.7533 

.7543 

.7569 

.7577 

.7602 

.7608 

.7632 

.7636 

.7658 

.7660 

.36 

.7639 

.7646 

.7671 

.7676 

.7700 

.7711 

.7725 

.7739 

.7752 

.7766 

.7779 

.7792 

3/8 

.37 

.7677 

.7702 

.7707 

.7730 

.7733 

.7755 

.7767 

.7781 

.7794 

.7807 

.7820 

.7832 

.38 

.7768 

.7791 

.7793 

.7815 

.7824 

.7837 

.7850 

.7862 

.7875 

.7888 

.7900 

.7912 

.39 

.7853 

.7874 

.7880 

.7892 

.7905 

.7918 

.7930 

.7942 

.7954 

.7966 

.7978 

.7990 

V5 

.40 

.8149 

.8161 

.8172 

.8182 

.8193 

.8204 

.8214 

.8224 

.8235 

.8244 

.8254 

.8264 

7A. 

.43 

.8242 

.8252 

.8263 

.  8273 

.8283 

.8293 

.8303 

.8312 

.8322 

.8331 

.8341 

.  8350 

.45 

.8582 

.8590 

.8598 

.8606 

.8614 

.8622 

.8629 

.8637 

.8644 

.8652 

.8659 

.8667 

Y2 

.50 

.8877 

.8883 

.8890 

.8896 

.8902 

.8908 

.8914 

.8920 

.8925 

.8931 

.8937 

.8942 

.55 

.8944 

.8950 

.8956 

.8962 

.8968 

.8973 

.8979 

.8984 

.8989 

.8995 

.9000 

.9005 

Vli 

.56 

.9132 

.9136 

.9141 

.9146 

.9150 

.9155 

.9159 

.9164 

.9168 

.9173 

.9177 

.9181 

3/5 

.60 

.9245 

.9,249 

.9253 

.9257 

.9261 

.9265 

.9269 

.9272 

.9276 

.9280 

.9284 

.9288 

Vs 

.62 

.9349 

.9352 

.9356 

.9359 

.9363 

.9366 

.9369 

.9373 

.9376 

.9379 

.9382 

.9385 

.65 

.9415 

.9418 

.9421 

.9424 

.9427 

.9430 

.9433 

.  9436 

.9438 

.9442 

.9444 

.9447 

2/3 

.66 

.9489 

.9491 

.9494 

.9497 

.9499 

.9502 

.9505 

.9507 

.9509 

.9512 

.9514 

.9517 

"A. 

.68< 

.9531 

.9533 

.9536 

.9538 

.9541 

.9543 

.9546 

.9548 

.9550 

.9552 

.9554 

.9557 

7Ao 

.70 

.9680 

.9682 

.9684 

.9685 

.9687 

.9688 

.9690 

.9691 

.9693 

.9695 

.9696 

.9698 

3/4 

.75 

MEAN   EFFECTIVE    PRESSURE   AND   POINT   OF   CUT-OFF 


117 


cutting    off    at     one-quarter    stroke,    and    exhausting    at    atmospheric 
pressure? 

By  the  table,  the  mean  pressure  per  pound  of  absolute  initial 
for  3  per  cent  clearance  and  one-quarter  cut-off  is  0.6148  of  the 
initial  pressure.  The  absolute  initial  is  90  +  14.7  =  104.7  Ibs.  The 


Absolute  Zero  of  1'ressure 

FIG.  104. 


mean  pressure  of  the  ideal  diagram  is  therefore  104.7X0.6148=64.37 
pounds.  This  is  the  mean  effective  pressure  represented  by  the  dia- 
gram ABODE  in  Fig.  104.  Since  there  is  14.7  pounds  back  pressure 
above  absolute  zero,  this  must  be  subtracted,  giving  64.37—14.7=49.67 
as  the  mean  effective  pressure  represented  by  the  area  ABCFG.  If 


FIG.  105. 


FIG.  106. 


the  engine  were  condensing  we  would  subtract  the  absolute  back  pres- 
sure corresponding  with  the  vacuum,  roughly  one  pound  for  each  two 
inches  of  vacuum  short  of  30  inches,  i.e.,  one  pound  for  28  inches,  two 
pounds  for  26  inches,  three  pounds  for  24  inches,  etc. 

More  accurate  values  may  be  found  in  a  table  of  the  Physical  Prop- 
erties of  Steam. 


118 


THE  STEAM  ENGINE   INDICATOR 


But  no  engine  makes  a  diagram  like  ABCFG;  the  steam  line  is  apt 
to  fall  away,  the  points  of  cut-off  and  release  to  be  rounded,  the  line  of 
counter-pressure  to  hang  up  in  places,  and  the  compression  takes  out 
considerable  area.  The  actual  mean  effective  pressure  will  be  to  the 
mean  effective  calculated  above  as  the  actual  diagram  which  the  engine 
would  make  is  to  the  ideal  area.  This  relationship  is  indicated  for  three 
typical  cases  in  Figs.  105,  106,  and  107  by  diagrams  which  give  the 
percentages  which  the  realized  area  bears  to  the  ideal.  If  in  the  above 
example  we  may  expect  the  engine  to  realize  about  90  per  cent  of  the 


FIG.  107. 

ideal  area,  we  may  say  the  probable  M.E. P. equals  about  49.67X0.9=44.7 
Ibs. 


To  FIND  THE  MEAN  EFFECTIVE  PRESSURE  FROM  THE 
TABLE 

RULE. — Multiply  the  tabular  value  opposite  the  given  point  of  cut-off 
and  in  the  column  of  the  given  clearance  by  the  absolute  initial  pressure; 
subtract  the  absolute  back  pressure  and  multiply  by  the  proportion  of  the 
ideal  area  probably  realized. 

The  initial  pressure  means  the  pressure  which  gets  into  the  cylinder, 
and  may  be  very  different  from  the  boiler  pressure,  especially  with 
a  throttling  governor. 


CHAPTER   XV 
STEAM  CONSUMPTION  FROM  THE  DIAGRAM 

KNOWING  the  cubic  capacity  of  the  cylinder  and  the  number  of  times 
it  is  filled  and  emptied  per  hour,  we  could,  if  the  entire  contents  of  the 
cylinder  remained  as  steam  all  the  time,  compute  the  cubic  feet  of  steam 
passing  through  the  engine  in  that  time.  Knowing  from  the  diagram 
the  pressure  of  this  steam  we  can  find  in  a  steam  table  the  weight  per 
cubic  foot,  and  thus  the  weight  of  steam  passed  per  hour.  The  dia- 
gram also  gives  us  a  measure  of  the  horse-power,  dividing  by  which 
we  get  the  number  of  pounds  of  steam  accounted  for  by  the  diagram 
per  hourly  horse-power.  This  will  be  always  less  than  the  actual  amount 
of  steam  supplied  to  the  engine,  because  a  considerable  proportion  of  such 
steam  is  condensed  on  its  entrance  to  the  cylinder,  and  is  not  re-evaporated 
until  after  the  valve  opens  for  exhaust,  so  that  it  does  not  show  as  steam 
upon  the  diagram  at  all.  The  computation  is  of  use,  however,  for  pur- 
poses of  comparison,  and  as  a  measure  of  the  minimum  amount  of  steam 
which  the  diagram  would  allow  per  horse-power,  and  should  be  under- 
stood by  one  who  desires  to  attain  proficiency  with  the  indicator. 

Let      A  =area  of  piston  in  square  inches, 
S=  length  of  stroke  in  feet, 
N  =  number  of  strokes  per  minute, 
P=mean  effective  pressure,  indicated  by  diagram. 
V=  volume  generated  by  the  piston  per  hour. 

V=~  XSXGON,   ........     (1) 

the  area  in  square  inches  divided  by  144  to  reduce  to  square  feet,  multi- 
plied by  the  length  of  the  stroke,  gives  the  cubic  feet  per  stroke,  and 
by  00  times  the  number  of  strokes  per  minute  gives  the  number  of  cubic 
feet  passed  through  by  the  piston  per  hour. 

The  horse-power  is  33QQQ .     (2) 

Dividing  equation  (1)  by  equation  (2)  we  get  the  number  of  cubic  feet 
passed  through  by  the  piston  in  an  hour  for  each  horse-power.  As  the 

119 


120 


THE  STEAM  ENGINE   INDICATOR 


area,  length  of  stroke,  and  number  of  strokes  per  minute  are  used  i] 
calculating  both  the  volume  and  the  horse-power  they  cancel  each  othe 
in  the  division,  and  the  formula  becomes 


PANS 
33000 


.4£60AT33000_  13750 
144PANS        ~P~' 


or  in  plain  language,  13,750  divided  by  the  mean  effective  pressure  wil 
give  the  cubic  feet  of  piston  displacement  per  hour  for  each  horse 
power  generated  by  any  engine,  whatever  its  size  or  speed.  Substitut 
ing  for  P  the  common  abbreviation  of  the  mean  effective  pressure  w< 
have 


13700 

=  volume  generated  per  hour  per  horse-power.    .     . 


(3 


If  the  engine  had  no  clearance  nor  compression  and  the  release  di( 
not  occur  until  the  end  of  the  stroke,  we  could  measure  the  pressure  o 


FIG.  108. 

the  steam  at  the  point  a,  Fig.  108,  find  in  a  steam  table  the  weight  o 
steam  of  that  pressure  per  cubic  foot,  multiply  the  volume  per  horse 
power  by  that  weight,  and  find  the  weight  per  horse-power  per  hour 
As  the  quantities  in  the  steam  tables  are  usually  given  in  pounds  absolut 
it  is  better  to  measure  from  the  zero  line  ox,  or  to  add  14.7  pounds  to  th' 
measurement  from  the  atmospheric  line.  Or  we  could  equally  we! 
measure  the.  pressure  at  any  other  point  after  the  cut-off  valve  closes 
and  take  such  proportion  of  the  volume  given  by  formula  3,  based  01 
the  whole  stroke,  as  the  portion  of  the  stroke  completed  by  the  pistoi 
up  to  the  point  chosen  bears  to  the  full  stroke.  If  we  measure  the  volum 
at  a  we  have  had  so  many  complete  cylinderfuls  of  steam  at  that  pres 
sure,  and  formula  (3)  will  give  the  volume  per  horse-power.  If  we  measur 


STEAM  CONSUMPTION   FROM  THE  DIAGRAM  121 

the  volume  at  half-stroke  6  we  have  had  only  one-half  the  volume  at  this 
higher  pressure,  and  formula  must  be  multiplied  by  0.5  to  give  the  num- 
ber of  cubic  feet  per  horse-power  per  hour, of  this  higher  pressure  steam. 
Likewise  if  we  measure  the  pressure  at  one-quarter  stroke  c  we  shall 
have  had  but  one-quarter  of  the  volume,  and  must  multiply  the  for- 
mula by  0.25,  and  so  for  any  other  fraction  of  the  stroke.  If  the  amount 
of  steam  in  the  cylinder  v/ere  constant  throughout  the  expansion  the 
weight  per  horse-power  per  hour  would  be  the  same  whether  we  meas- 
ured it  at  cut-off  or  at  release,  or  at  any  point  between,  but  condensa- 
tion and  re-evaporation  are  going  on,  so  that  there  is  more  steam  in  the 
cylinder  later  in  the  stroke  than  immediately  after  the  cut-off,  and  there 
will  usually  be  found  to  be  a  greater  amount  of  steam  accounted  for 
per  horse-power  per  hour  the  nearer  the  measurements  are  made  to  the 
point  of  release.  Call  the  fraction  of  the  stroke  completed  at  the  point 
chosen  F,  and  the  weight  of  steam  per  cubic  foot  at  that  pressure  wf, 
then  under  the  simple  conditions  assumed 

137°°          =lbs.  steam  per  H.P.H (4) 


M.E.P. 

when  the  pressure  is  measured  at  the  end  of  the  stroke,  as  at  a,  F  becom.es 
unity  or  one,  and  the  formula  becomes 


„ 
=lbs.  steam  per  H.P.H.     .....     (o) 

^.i  . 

We  have  yet  to  determine  the  amount  of  steam  required  to  fill  the 
clearance,  and  the  amount  left  in  the  c}dinder  when  the  exhaust  valve 
closes.  As  we  cannot  exhaust  into  a  perfect  vacuum  there  will  always 
be  some  such  steam,  even  when  there  is  no  compression.  Suppose 
the  engine  to  have  five  per  cent  clearance,  then  when  the  piston  was 
at  a  instead  of  having  the  volume  swept  through  by  the  piston  behind 
it  we  should  have  1.05  times  that  volume.  When  the  piston  was  at 
half-stroke  we  should  have  instead  of  0.5  of  the  piston  displacement 
0.55  of  that  volume,  and  generally  for  any  fraction  F  of  the  stroke  com- 
pleted at  the  point  chosen  for  measurement  we  should  have  F  +c  of 
the  piston  displacement  behind  it,  c  being  the  clearance  in  fractions 
of  the  stroke,  and  the  steam  per  horse-power  per  hour  becomes 

13750  Wf.  (6) 


M.E.P. 


Suppose  in  Fig.  109  the  exhaust  valve  to  close  at  e  when  the  return 
stroke  is  0.8  completed.     The  volume  of  steam  shut  in  would  be  the  area 


122 


THE   STEAM   ENGINE   INDICATOR 


of  the  piston  in  square  feet  multiplied  by  the  fraction  of  stroke  uncom- 
pleted plus  the  five  one-hundredths  of  the  stroke,  included  in  the  clearance, 
that  is,  0.2+0.05=0.25;  or  generally,  calling  the  portion  of  the  stroke 
uncompleted  at  the  compression  x,  the  volume  inclosed  would  be,  per 
hour, 

A 

•**•  /  .  \        s*s~i    IT  /^7\ 


144 


40  Scale 
M.E.P.47.6  Ibs. 


Steam  Consumption  =  18.08  Ibs. 
per  h.pJi. 


8.6  inches 


4  inches 


FIG.  109. 

PANS 

and  this  divided  by  the  horse-power      f  to  give  the  volume  saved 

ooOUO 

per  horse-power,  and  multiplied  by  the  weight  wx  of  steam  per  cubic 
foot  at  the  pressure  obtained  at  the  point  x  would  be 

13750 


M.E.P.(aH      *» 

Subtracting  this  from  formula  (6)  we  have 


(8) 


(9) 


Where    c=  clearance  in  fractions  of  the  stroke; 

F=  fraction  of  stroke  completed  at  point  chosen  on  expansion  line: 
x=  fraction  of  stroke  uncompleted  at  point  chosen  on  compres- 

line 

it>  =wt.  per  cu.ft.  of  steam  at  pressure  measured  at  F\ 
wx=v/t.  per  cu.ft.  of  steam  at  pressure  measured  at  x; 
Q=steam  accounted  for  per  H.P.  per  hour. 


STEAM  CONSUMPTION  FROM  THE  DIAGRAM  123 

RULE. — To  the  fraction  of  the  forward  stroke  completed  at  the  point 
chosen  add  the  clearance,  also  in  fractions  of  the  stroke,  and  multiply  the 
sum  by  the  weight  per  cubic  foot  of  steam  of  the  pressure  measured  at  this 
point.  (Product  1.} 

To  the  fraction  of  the  return  stroke  uncompleted  at  the  point  chosen  on 
the  compression  line  add  the  clearance,  expressed  as  before,  and  multiply 
the  sum  by  the  weight  per  cubic  foot  of  steam  of  the  pressure  measured  at 
this  point.  (Product  2.} 

Multiply  the  difference  between  products  1  and  2  by  the  quotient  of  13,750 
divided  by  the  M.E.P.;  the  final  product  will  be  the  number  of  pounds  vf 
steam  per  hour  per  horse-power  accounted  for  by  the  diagram. 

As  an  assistance  in  working  with  the  above  rule  or  formula  Table  VI 
gives  the  value  of  13,750  divided  by  mean  effective  pressures  of  from 
10  to  100  pounds.  The  first  column  under  zero  gives  the  quotients  for 
even  pounds,  the  succeeding  columns  for  additional  tenths  of  pounds. 

Thus  the  quotient  of  would  be  found  in  the  horizontal  line  with 

oo.o 

35  and  in  the  column  under  6  to  be  386.23. 

EXAMPLE. — The  diagram  shown  in  Fig.  109  shows  with  a  40  scale  a 
M.E.P.  of  47.5  pounds;  clearance  5  per  cent.  How  much  steam  is 
accounted  for  per  horse-power  per  hour? 

Let  us  select  the  points  F  and  x  from  which  to  make  our  measure- 
ments. The  whole  length  of  the  diagram  is  4  inches,  the  length  to  the 
point  F,  3.5  inches.  The  fraction  F  of  the  stroke  completed  at  this 

point  is  therefore  '-j-  =0.875.     The  distance  xa  equals  0.4  of  an  inch, 

0.4 

and  the  fraction  of  the  return  stroke  uncompleted  at  the  point  x  is  — ^-  =0.1. 

The  pressure  (absolute)  at  F  is  32  pounds,  at  x  19  pounds.  The 
weight  of  steam  per  cubic  foot  at  32  pounds  is  0.0789,  at  19  pounds 
0.0483. 

then  c-0.05 

7^=0.875 
x=0.l 
wf  =0.0789 
wx=  0.0483 
and       M.E.P.  =   .47.5 

The  steam  accounted  for  per  horse-power  per  hour  is 

x[(0.875  +  0.05)0.0789-  (0.1  +0.05)0.0483].' 
47.5 


124 


THE   STEAM   ENGINE   INDICATOR 


From  the  table  we  find  the  value  of  -p=-v-  to  be  289.47,  and  we  have 

47.5 

289.47X[(0.925X0.0789) -(0.15X0.0483)] -19.03    pounds  of    steam   per 
hour  for  each  horse-power. 

It  is  not  necessary  that  the  point  X,  at  which  the  pressure  of  the  steam 
saved  by  compression  is  measured,  shall  be  at  the  commencement  of 
compression.  It  may  be  located  at  any  point  upon  that  line  or  upon 


.05  > 


\ 


\ 

X2\J 


FIG.  110. 

the  dotted  continuation  of  that  line  into  the  clearance  space.  In  Fig. 
110,  representing  the  compression  corner  of  a  diagram  on  a  large  scale 
let  the  vertical  divisions  represent  hundredths  of  the  stroke,  the  clearance 
C  being  five  per  cent  or  five  hundredths,  and  the  exhaust  valve  closing 
at  X  when  ten  one-hundredths  of  the  stroke  are  uncompleted.  When 
the  exhaust  valve  closes  we  have  a  volume  of  steam  inclosed  equal  to 
C+X =0.05  +0.10  =0.15  of  the  displacement  at  the  pressure  X,  or  if 
we  measure  at  X1,  when  0.08  of  the  stroke  remain  to  be  completed,  we 
shall  have  0.05 +  .08  =0.13  at  the  pressure  X,1  or  0.10  at  the  pressure  X2, 
or  0.05  at  the  pressure  X3,  0.03  at  X4,  etc.,  so  that  so  long  as  we  measure 


VALUES   OF 


STEAM   CONSUMPTION   FROM   THE   DIAGRAM 

TABLE   VI 
13750 


125 


M.E.P. 


FOR  COMPUTING   STEAM   CONSUMPTION 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1375.00 

1361.39 

1348.04 

1334.95 

1322.15 

1309.52 

1297.17 

1285.04 

1273.14 

1261.46 

11 

1250.00 

1238.74 

1227.68 

1216.81 

1206.13 

1195.65 

1185.34 

1175.19 

1165.25 

1155.46 

12 

1145.83 

1136.36 

1127.05 

1117.88 

1108.87 

1100.00 

1091.11 

1082.67 

1074.21 

1062.01 

13 

1057.69 

1049.62 

1041.66 

1033.83 

1026.12 

1018.51 

1011.03 

1003.64 

996.38 

989.21 

14 

982.14 

975.18 

968.31 

961.54 

954.86 

948.29 

941.78 

935.37 

929.00 

922.82 

lo 

916.67 

910.60 

904.61 

898.69  893.05 

867.09 

881.41 

875.79 

870.25 

864.77 

16 

871.87 

854.04 

848.76 

843.55 

838.41 

833.33 

828.31 

823.35 

818.45 

813.61 

17 

808.82 

804.09 

799.42 

794.79 

790.23 

785.71 

781.25 

776.84 

772.47 

768.15 

18 

763.89 

759.67 

755.49 

751.36 

747.28 

743.24 

739.24 

735.29 

731.38 

727.51 

1!' 

723.68 

719.89 

716.15 

712.43 

708.76 

705.13 

701.53 

697.99 

694.44 

690.95 

20 

687.50 

683.08 

680.69 

677.34 

674.02 

670.73 

667.47 

664.25 

661.06 

657.84 

21 

654.76 

651.66 

648.58 

645.54 

642.52 

639.53 

636.57 

633.64 

630.73 

627.85 

22 

625.00 

622.17 

619.37 

616.59 

613.94 

611.11 

608.41 

605.72 

603.07 

600.43 

23 

597.83 

595.24 

592.67 

590.12 

587.61 

585.11 

582.62 

580.16 

577.73 

575.31 

24 

572.92 

570.54 

568.18 

565.84 

563.52 

561.22 

558.94 

556.67 

554.43 

552.21 

25 

550.00 

547.81 

545.64 

543.47 

541.33 

539.21 

537.11 

535.02 

532.94 

530.88 

26 

528.85 

526.82 

524.81 

522.81 

520.83 

518.87 

516.91 

514.98 

513.06 

511.15 

27 

509.26 

507.38 

505.51 

503.66 

501.82 

500.00 

498.11 

496.39 

494.60 

493.19 

2S 

491.07 

489.32 

487.55 

485.86 

484.15 

482.45 

480.76 

479.09 

477.43 

476.12 

29 

474.14 

472.51 

470.89 

469.28 

467.68 

466.10 

464  .  53 

462.89 

461.40 

459.86 

30 

458.33 

456.81 

455.30 

453.79 

452.30 

450.82 

449.34 

447.88 

446.42 

444.98 

31 

443.55 

442.12 

441.99 

439.30 

437.83 

436.51 

435.12 

433.75 

432.39 

431.35 

32 

429.69 

428.35 

427.01 

425.69 

424.38 

423.07 

421.77 

420.49 

419.21 

417.93 

33 

416.67 

415.41 

413.85 

412.91 

411.67 

410.44 

409.22 

408.01 

406.80 

405.60 

34 

404.41 

403.22 

402.05 

400.87 

399.71 

398.55 

397.39 

396.25 

395.11 

393.98 

35 

392.84 

391.73 

390.63 

389.51 

388.41 

387.32 

386.23 

385.15 

384.08 

383.01 

36 

381.94 

380.89 

379.83 

378.78 

377.75 

376.71 

375.68 

374.66 

373.64 

372.62 

37 

371.62 

370.62 

369.62 

368.63 

367.65 

366.66 

365.69 

364.72 

363.75 

362.79 

38 

361.84 

360.89 

359.94 

359.00 

358.07 

357.40 

356.22 

355.29 

354.38 

353.47 

39 

352.56 

351.64 

350.77 

349.87 

348.98 

348.10 

347.22 

346.34 

345.47 

344.11 

40 

343.75 

342.89 

342.32 

341  .  19 

340.34 

339.51 

338.67 

337.83 

337.01 

336.18 

41 

335.36 

334.55 

333.74 

332.92 

332.12 

331.32 

330.52 

329.71 

328.94 

328.16 

42 

327.38 

326.36 

325.83 

325.06 

324.26 

323  .  50 

322.77 

322.01 

321.35 

320.51 

43 

319.77 

319.02 

318.29 

317.55 

316.82 

316.09 

315.36 

314.64 

313.92 

313.21 

41 

312.50 

311.79 

311.09 

310.38 

309.68 

308.98 

308.29 

300.61 

306.92 

306.23 

45 

305.55 

304.88 

304.20 

303.55 

302.86 

302.19 

301.53 

300.87 

300.22 

299.34 

46 

298.91 

298.26 

297.62 

296.97 

296.33 

295.48 

295.06 

294.43 

293.80 

292.96 

47 

292.55 

291.93 

291.31 

290.61 

290.08 

.  289.47 

288.86 

288.26 

287.65 

287.05 

4N 

286.46 

285.86 

285.26 

284.66 

284.09 

283.50 

282.92 

282.34 

281.76 

281.18 

49 

280.61 

280.04 

279.47 

278.09 

278.34 

277.77 

277.21 

276.66 

276.10 

275.55 

50 

275.00!  274.45 

273.90 

273.35 

272.82 

272.27 

271.73 

271.20 

270.67 

270.13 

51 

269.61  269.08 

268.55 

268.03 

267.51 

266.99 

266.47 

265.95 

265.44 

264.93 

52 

264.  43  1  263.91 

263.41 

262.91 

262.40 

261.90 

261.40 

260.91 

260.41 

258.03 

63 

259.43 

258.94 

258.45 

257.97 

257.49 

257.00 

256.53 

256.05 

255.57 

255.10 

54 

254.63 

254.16 

253.69 

253.22 

252.75 

252.29 

251.83 

251.37 

250.91 

250.47 

55 

250.00  249.54 

249.09 

248.64 

248.19 

247.74 

247.30 

246.86 

246.41 

245.97 

126  THE   STEAM   ENGINE   INDICATOR 

TABLE    VI — Continued 
VALUES   OF   ~          FOR  COMPUTING   STEAM   CONSUMPTION 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

56 

244  .  64 

245.10 

244.66 

244.22 

243.79 

243.36 

242.93 

242.50 

242  .  07 

241.65 

57 

241.23 

240.80 

240.38 

239.26 

237.80 

239.13 

238.71 

238.30 

237  .  88 

237.47 

58 

233.62 

236  .  66 

236.25 

235.84 

235.44 

235.04 

234.64 

234  .  22 

233  .  84 

233.44 

59 

237.07 

232.64 

232  .  26 

231.87 

231.84 

231.09 

230.71 

230.31 

229  .  93 

229.54 

60 

229.17 

228.79 

228.41 

228.03 

227.65 

227  .  27 

226.89 

226.52 

226.15 

225.78 

61 

225.41 

225.04 

224.67 

224.30 

223.92 

223.57 

223.21 

222.85 

222.49 

222.13 

62 

221.71 

221.42 

221.06 

220.67 

220.35 

220.00 

219.64 

219.29 

218.93 

218.  6C 

63 

218.25 

217.91 

217.56 

217.21 

216.87 

216.53 

216.19 

215.06 

215.51 

215.18 

64 

214.84 

214.50 

214.17 

213.99 

213.50 

213.17 

212.69 

212.51 

212.19 

211.86 

65 

211.54 

211.21 

210.88 

210.56 

210.44 

209.92 

209.60 

209  .  28 

208.96 

208.64 

66 

208.31 

208.01 

207.70 

207.39 

207.08 

206.70 

206.45 

206.14 

205.83 

205.53 

67 

205.22 

204.91 

204.61 

204  .  31 

204.00 

203  .  70 

203.40 

203.10 

202.80 

202.  5C 

68 

202.20 

201.91 

201.61 

201.32 

201.04 

200.73 

200.43 

200.14 

199.85 

199.56 

69 

199.27 

198.98 

198.69 

198.41 

198.12 

197.84 

196.12 

197  .  56 

196.99 

196.  7C 

70 

196.43 

196.14 

195.86 

195.59 

195.31 

195.03 

194.75 

194.34 

194.21 

193.93 

71 

193.66 

193.39 

193.12 

192.84 

192.57 

192.31 

192.03 

191.77 

191.50 

191.23 

72 

190.97 

190.71 

190.44 

190.17 

189.91 

189.65 

189.39 

189.13 

188.87 

187.24 

73 

188.36 

188.10 

187.84 

187.58 

187.33 

187.07 

186.82 

186.56 

186.31 

186.  oe 

74 

185.80 

185.56 

185.30 

185.06 

184.81 

184  .  56 

184.31 

184  .  07 

183.82 

183.57 

75 

183.34 

183.09 

182.84 

182.60 

182.36 

182.11 

181.87 

181.63 

181.39 

181.  1C 

76 

180.92 

180.68 

180.45 

180.21 

179.97 

179.73 

179.50 

179.27 

179.03 

178.  8C 

77 

178.57 

178.34 

178.11 

177.87 

177.65 

177.42 

177.19 

177.09 

176.73 

176.51 

78 

176.28 

176.05 

175.83 

175.61 

175.38 

175.16 

174.81 

174.71 

174.49 

174.27 

79 

174.05 

173.83 

173.61 

173.39 

173.17 

172.95 

172.73 

172.52 

172.18 

172.  0£ 

80 

171.87 

171.66 

171.45 

171.23 

171.02 

170.81 

170.59 

170.38 

170.17 

169.96 

81 

169.75 

169.54 

169.33 

169.12 

168.91 

168.71 

168.50 

168.29 

168.09 

167.  8£ 

82 

167.68 

167.47 

167.27 

167.07 

166.86 

166.67 

166.46 

166.26 

166  .  06 

165.  8e 

83 

165.66 

165.46 

165.26 

165.06 

164  .  86 

164.67 

164.47 

164.27 

164.09 

163.  8£ 

84 

163.69 

163.49 

163.30 

163.11 

162.92 

162.72 

162.52 

162.22 

162.14 

161.  9e 

85 

161.76 

161.57 

161.38 

161.19 

161.01 

160.82 

160.63 

160.44 

160.25 

160.07 

86 

159.88 

159.70 

159.51 

159.33 

159.14 

158.73 

158.77 

158.59 

158.41 

158.  2£ 

87 

158.04 

157.86 

157.68 

157.50 

157.32 

157.14 

156.96 

156.78 

156.61 

156.44 

88 

156.25 

156.07 

155.89 

155.71 

155.54 

155.36 

155.19 

154.01 

154.84 

154.66 

89 

154.49 

154.32 

154.14 

153.97 

153.80 

153.63 

153.46 

153.29 

153.12 

152.94 

90 

153.78 

152.61 

152.44 

152.27 

152.10 

151.93 

151.76 

151.60 

151.54 

151.  2( 

91 

151.09 

150.93 

150.77 

150.60 

150.43 

150.27 

150.11 

149.94 

149.77 

149.61 

92 

149.45 

149.29 

149.13 

148.97 

148.81 

148.64 

148.48 

148.32 

148.16 

148.  0( 

93 

147.85 

147.58 

147.53 

147.25 

147.21 

147.05 

146.90 

146.73 

146.59 

146  .  4«r 

94 

146.27 

146.12 

145.96 

145.81 

145.65 

145.50 

145.34 

145.19 

145.04 

144  .  8< 

95 

144.73 

144.58 

144.48 

144.28 

144.13 

143.98 

143.82 

143.67 

143.52 

143.3^ 

96 

143.23 

143.08 

142.93 

142.67 

142.63 

142.48 

142.34 

142.19 

142.04 

141.  9( 

97 

141.75 

141.61 

141.46 

141.31 

141.17 

141.02 

140.88 

140.73 

140.59 

140.4^ 

98 

140.31 

140.17 

140.02 

139.87 

139.73 

139.59 

139.46 

139.31 

139.17 

139.(X 

99 

138.88 

138.74 

138.61 

138.46 

138.33 

138.19 

138.05 

137.91 

137.77 

137.6; 

100 

137.50 

137.36 

137.22 

137.09 

136.95 

136.81 

136.68 

136.54 

136.41 

136.2' 

STEAM  CONSUMPTION   FROM   THE   DIAGRAM 


127 


the  pressures  and  volumes  accordingly  X  may  be  located  anywhere  on  the 
compression  curve,  or  even  on  the  dotted  extension  of  that  line  inside 
the  clearance  space.  The  compression  after  the  piston  has  reached  the 
end  of  its  stroke  will  go  on  by  the  admission  of  the  higher  pressure  steam. 
Suppose  in  Fig.  Ill  the  exhaust  valve  closes  at  E,  shutting  in  a  volume 
proportional  to  the  line  OE,  of  exhaust  steam.  When  the  piston  reaches 
the  end  of  its  stroke  on  the  line  A  a  the  clearance  will  be  full  of  steam 
raised  by  compression  to  the  pressure  B.  The  admission  valve  being 
now  opened,  live  steam  rushes  in  and  raises  the  pressure  to  that  of  the 
steam  line  AC,  by  which  process  the  steam  saved  by  compression  and 
which  occupied  the  whole  clearance  at  a  pressure  B  before  admission 
g  h  is  compressed  to  a  volume  proportional  to 

the  line  gh,  corresponding  with  the  pressure 
to  which  it  is  subjected.     At  this  pressure, 
it  will  be  seen,  it  occupies  three-sevenths 
of  the  clearance  space,  and  the  remain- 
ing four-sevenths  must  be  supplied  from 
the  boiler.     The  amount  of  new  steam 
supplied  up  to  the    point    of    cut-off 
then  is   proportional    to    the    line 
hC.     When   the   pencil   reached 
D  the  compression  steam  had 
B  ^      expanded     to    a    volume 


FIG.  111. 

proportional  to  ed,  corresponding  with  that  pressure,  and  the  new 
steam  involved  in  the  stroke  is  proportional  to  the  line  Dd,  and 
this  is  true  of  any  line  drawn  horizontally  across  the  diagram 
between  the  expansion  and  compression  line,  or  the  continuation 
of  the  latter  into  the  clearance.  This  fact,  when  the  compression 
is  such  that  a  horizontal  line  from  the  point  which  we  wish  to  use  on 
the  expansion  line  will  cut  the  compression  line,  as  Fx,  gives  a  simple 
process  for  finding  the  steam  accounted  for  by  the  indicator  corrected 
both  for  clearance  and  compression.  It  will  be  remembered  that  the 
formula  when  the  whole  volume  of  the  displacement  was  involved  and 
the  pressure  taken  at  the  end  of  the  stroke  t  was  by  formula  (5), 

13750w 
M.E.P.' 


128  THE   STEAM   ENGINE   INDICATOR 

where  w  was  the  weight  per  cubic  foot  of  steam  at  the  terminal  pressure. 
If  instead  of  measuring  the  pressure  at  the  terminus  of  the  stroke  t, 
we  take  any  other  time  point,  as  F  or  D,  the  volume  involved  will  be 
to  the  whole  displacement  volume  as  xF  or  dD  is  to  the  length  of  the 
diagram  ay.  If  as  before  F  =the  fraction  of  the  stroke  completed  at 
the  point  chosen  for  measurement,  as  F,  Fig.  Ill,  and  X=the  portion 
of  the  return  stroke  uncompleted  at  the  point  chosen  on  the  com- 
pression line,  then  F  —  X  (i.e.,  jF  —  jX,  Fig.  Ill)  will  be  the  fraction 
of  the  whole  length  of  the  diagram  occupied  by  the  line  XF,  included 
between  the  expansion  and  compression  lines.  Substituting  for  w  in 
formula  (5)  w/  =  the  weight  per  cubic  foot  at  the  pressure  measured 
at  point  F,  and  multiplying  by  the  fraction  F  —  X,  we  get  the  steam 
accounted  for  per  horse-power  and  per  hour,  reducing  the  complete 
formula  to 

13750    . 


RULE.  —  From  the  fraction  of  the  stroke  completed  at  the  point  chosen 
on  the  expansion  line  subtract  the  fraction  of  the  stroke  uncompleted  at 
the  point  on  the  compression  line  which  is  in  the  same  horizontal  line.  Mul- 
tiply the  difference  by  the  weight  per  cubic  foot  of  steam  at  the  pressure 
measured  at  the  points  chosen  and  by  the  quotient  of  13,750  divided  by  the 
mean  effective  pressure.  The  final  product  will  be  the  weight  of  steam 
accounted  for  per  horse-power  per  hour. 

When  the  terminal  pressure  is  so  high  or  the  compression  is  so  small 
that  a  horizontal  line  would  cut  the  admission  rather  than  the  com- 
pression line,  the  point  X  will  be  independently  located  and  formula  (9) 
used  rather  than  to  construct  the  extension  of  the  compression  line  into 
the  clearance,  though  the  simple  method  just  described  would  still  be 
used  on  speculative  or  theoretical  work.  If  the  horizontal  line  intersects 
the  junction  of  the  compression  and  admission  lines  as  at  B,  the  portion 
X  of  the  stroke  uncompleted  at  this  point  becomes  zero.  If  the  hori- 
zontal line  crosses  the  admission  line,  as  at  Dd,  X  becomes  minus,  and 
the  .distance  from  the  admission  line  A  a  to  the  point  d  where  the  hori- 
zontal crosses  the  compression  line  must  be  added  to  F.  The  value 
F—X,  however,  would  in  this  case  be  more  easily  arrived  at  and  may 
be  found  in  any  case  by  dividing  the  length  of  the  horizontal  line,  as 
dD,  included  between  the  expansion  lines,  by  the  length  of  the  diagram  ay. 

RULE.  —  Draw  a  line  across  the  diagram  parallel  with  the  atmospheric  line. 
Divide  the  length  of  that  portion  of  this  line  included  between  the  expansion 
and  compression  lines  by  the  extreme  length  of  the  diagram,  and  multiply 
the  quotient  by  the  weight  per  cubic  foot  of  steam  at  the  pressure  indicated 
by  the  height  of  the  horizontal  line.  Multiply  this  product  by  the  quotient 


STEAM  CONSUMPTION  FROM  THE  DIAGRAM  129 

of  13,750  divided  by  the  mean  effective  pressure,  and  the  result  will  be  the 
pounds  of  steam  accounted  for  per  horse-power  per  hour. 

This  rule  is  identical  with  the  other,  the  proportion  of  the  line  of 
quantities  to  the  length  of  the  diagram  being  arrived  at  differently. 
It  can  be  deduced  from  the  formula  algebraically  as  follows:  When 
the  points  F  and  X  are  at  the  same  height  wx=wf,  and  the  formula 
becomes 


STEAM  ACCOUNTED  FOR  BY  MULTIPLE-CYLINDER  DIAGRAMS. 

We  have  seen  that  the  amount  of  steam  in  the  cylinder  is  different 
at  different  points  in  the  stroke,  increasing  by  re-evaporation  as  the 
stroke  progresses.  The  same  thing  holds  true  in  a  multiple-cylinder 
engine.  A  portion  of  steam  is  measured  off  by  the  cut-off  valve  of  the 
high-pressure  cylinder.  This  portion  in  passing  through  the  series  of 
cylinders  develops  a  determined  amount  of  power.  If  the  quantity  of 
steam  remained  constant  the  quantity  per  horse-power  hour  would  be 
the  same  whether  measured  immediately  on  the  closure  of  the  high- 
pressure  cut-off  valve  or  just  before  its  final  release  in  the  low-pressure 
cylinder.  But  its  quantity  is  constantly  changing  and  more  steam  will 
be  found  to  be  accounted  for  per  horse-power  hour  at  the  terminal  end 
of  the  low-pressure  than  at  any  other  point,  under  ordinary  conditions. 
The  steam  accounted  for  may  be  computed  at  any  point  between  cut-off 
and  release  on  a  diagram  from  any  cylinder  by  the  same  rules  and 
formulas  used  for  simple  engines,  but  in  order  that  the  area,  stroke 
and  number  of  revolutions  may  cancel,  as  shown,  that  M.E.P.  must  be 
used  which  would  be  equivalent  in  effect  in  the  cylinder  with  which 
we  are  working  to  the  aggregate  of  the  several  mean  effectives  in  their 
respective  cylinders. 

The  effect  of  a  given  mean  effective  pressure  is  proportionate  to  the 
displacement  per  unit  of  time  of  the  cylinder  in  which  it  works.  A 
given  mean  effective  pressure  will  produce  twice  the  power  in*  a  cylinder 
having  twice  the  area,  with  the  same  piston  speed.  So  if  it  is  wished 
to  find  how  much  M.E.P.  would  be  necessary  to  develop  an  amount 
of  power  in  the  low-pressure  cylinder  equivalent  to  that  developed  by  a 
given  M.E.P.  in  the  high,  the  M.E.P.  must  be  divided  by  the  ratio  of  the 
displacements  between  the  high-  and  low-pressure  cylinders.  To  find 
this  ratio  multiply  the  square  of  the  diameter,  the  stroke,  and  the  revolu- 
tions per  minute  of  each  cylinder  together,  and  divide  the  product  from 
the  larger  cylinder  by  that  from  the  smaller.  As  in  ordinary  multi- 


130  THE   STEAM   ENGINE   INDICATOR 

cylinder  engines  all  the  cylinders  have  the  same  length  of  stroke  an 
number  of  revolutions  per  minute,  these  factors  cancel,  and  the  oper; 
tion  is  reduced  to  dividing  the  square  of  the  diameter  of  the  larg( 
cylinder  by  the  square  of  the  diameter  of  the  smaller,  or  dividing  tl 
larger  by  the  smaller  diameter  and  squaring  the  quotient. 

RULE. — To  refer  the  mean  effective  pressure  of  one  cylinder  to  anothe 
multiply  the  given  M.E.P.  by  the  ratio  between  the  cylinder  displacemen 
if  the  cylinder  to  which  it  is  to  be  referred  is  smaller,  or  divide  if  it  is  i\ 
larger. 

EXAMPLE. — In  a  compound  engine  having  cylinders  12  and  24  inch 
in  diameter,  running  at  the  same  piston  speed,  the  diagrams  show  \ 
pounds  of  M.E.P.  in  the  high-pressure  and  9.18  pounds  in  the  low.  Ref 
the  mean  effective  pressure  to  the  low-pressure  cylinder. 

The  ratio  between  the  cylinders  is 

(24  -5-12)2=4. 

Then  38  pounds  in  the  high-pressure  cylinder  would  be  equaled  1 
38-^4=9.5  pounds  in  the  low  pressure.  Add  this  to  the  9.18  poun 
shown  by  the  low-pressure  diagram  and  we  have  9.5  +9.18  —  18.68  poun 
of  mean  effective  pressure  which  would  be  required  to  do  in  the  lo1 
pressure  cylinder  alone  the  work  of  38  in  the  high  and  9.18  in  the  lo 
In  working  out  the  steam  accounted  for  per  horse-power  per  hour  fro 
the  low-pressure  diagram  therefore  the  M.E.P.  used  would  be  18. ' 
pounds. 

When  working   from   the  high-pressure  diagram  the   M.E.P.  of  t 
low-pressure   diagram   must   be   referred    to   the   smaller   cylinder.      ( 
account  of   the   smaller   displacement,  it  would   require   four   times 
much  pressure   (4  is  the  ratio  between  the  cylinder  displacements) 
do  the  work  in  the  high-pressure  cylinder  as  in  the  low,  so  that  to  < 
the  work  of   9.18  pounds   M.E.P.   in  the  low-pressure   cylinder  wou 
require  4X9.18  =36.72  in  the  high.     Add  to  this  the  38  pounds  indicati 
by  the  high-pressure  diagram  and  find  36.72+38=74.72  pounds  as  t] 
M.E.P.   to  be  used  in  the  formula  when  the  steam    accounted  for 
computed  from  the  high-pressure  diagram.     With  a  triple-  or  quadrupl 
expansion  engine  proceed  the  same  way. 

With  this  aggregate  M.E.P.  proceed  as  though  the  diagram  we 
from  a  single-cylinder  engine.  When  the  mean  effective  is  referred 
the  high-pressure  cylinder  it  is  liable  to  become  much  larger  than  ai 
actually  obtained,  and  to  exceed  the  limit  of  the  values  given  in  Table  V 
We  therefore  publish  Table  VII,  taken  from  the  Ashcroft  book  of  instru 
tions  for  the  Tabor  indicator  (a  continuation  of  that  table),  giving  tl 

13750 
values  of  .,  _,  _.  for  mean  effective  pressures  from  100  to  250  pounds. 


STEAM  CONSUMPTION  FROM  THE  DIAGRAM 


131 


If  instead  of  making  a  table  of 


13750 


for  various  mean  effective 


M.E.P. 

pressures  we  make  one  of  I3,7o0w  for  various  values  of  w,  we  avoid 
using  a  table  to  find  the  weight  per  cubic  foot  of  steam.  Such  a  table, 
computed  by  J.  W.  Thompson,  M.E.,  is  printed  on  page  132.  Finding 
in  this  table  the  value  for  the  pressure  at  the  point  chosen  for  measure- 
ment, divide  it  by  the  M.E.P.  and  multiply  the  quotient  by  F  —  X,  or 
by  the  ratio  of  the  horizontal  line  across  the  diagram  to  the  total  length 
of  the  diagram.  When  points  on  the  expansion  and  compression  lines 
are  at  different  heights  the  other  process  will  be  more  convenient. 


TABLE  VII 

13750 


VALUE   OF 


M.E.P. 


M.E.P. 
Lbs. 

13750 

M.E  P. 
Lbs. 

13750 
M.E.P. 

M.E.P. 
Lbs. 

13750 

M.E.P. 
Lbs. 

13750 

M.E.P. 
Lbs. 

13750 

M.E.P. 

M.E.P. 

M.E.P. 

M.E.P. 

101 

136.1 

131 

104.9 

161 

85.4 

191 

71.9 

221 

62.2 

102 

134.8 

132 

104.1 

162 

84.8 

192 

71.6 

222 

61.9 

103 

133.4 

133 

103.3 

163 

84.3 

193 

71.2 

223 

61.6 

104 

132.2 

134 

102.6 

164 

83.8 

194 

70.8 

224 

61.3 

105 

130.9 

135 

101.8 

165 

83.3 

195 

70.5 

225 

61.1 

106 

129.7 

136 

101.1 

166 

82.8 

196 

70.1 

226 

60.8 

107 

128.5 

137 

100.3 

167 

82.3 

197 

69.7 

227 

60.5 

108 

127.3 

138 

99.6 

168 

81.8 

198 

69.4 

228 

60.3 

109 

126.1 

139 

98.9  ! 

169 

81.3 

199 

69.0 

229 

60.0 

110 

125.0 

140 

98.2 

170 

80.8 

200 

68.7 

230 

59.7 

111 

123.8 

141 

97.5 

171 

80.4 

201 

68.4 

231 

59.5 

112 

122.7 

142 

96.8 

172 

79.9 

202 

68.0 

232 

59.2 

113 

122.6 

143 

96.1 

173 

79.4 

203 

67.7 

233 

59.0 

114 

120.6 

144 

95.4 

174 

79.0 

204 

67.4 

234 

58.7 

115 

119.5 

145 

94.8 

175 

78.5 

205 

67.0 

235 

58.5 

116 

118.5 

146 

94.1 

176 

78.1 

206 

66.7 

236 

58.2 

117 

117.5 

147 

93.5 

177 

77.6 

207 

66.4 

237 

58.0 

118 

116.5 

148 

92.9 

178 

77.2 

208 

66.1 

238 

57.7 

119 

115.5 

149 

92.2 

179 

76.8 

209 

65.7 

239 

57.5 

120 

114.5 

150 

91.6 

180 

76.3 

210 

65.4 

240 

57.2 

121 

113.6 

151 

91.0 

181 

75.9 

211 

65.1 

241 

57.0 

122 

112.7 

152 

90.4 

182 

75.5 

212 

64.8 

242 

56.8 

123 

111.7 

153 

89.8 

183 

75.1 

213 

64.5 

243 

56.5 

124 

110.8 

154 

89.2 

184 

74.7 

214 

64.2 

244 

56.3 

125 

110.0 

155 

88.7 

185 

74.3 

215 

63.9 

245 

56.1 

126 

109.1 

156 

88.1 

186 

73.9 

216 

63.6 

246 

55.8 

127 

108.2 

157 

87.5 

187 

73.5 

217 

63.3 

247 

55.6 

128 

107.4 

158 

87.0 

188 

73.1 

218 

63.0 

248 

55.4 

129 

106.5 

159 

86.4 

189 

72.7 

219 

62.7 

249 

55.2 

130 

105.7 

160 

85.9 

190 

72.3 

220 

62.5 

250 

55.0 

132 


THE   STEAM   ENGINE   INDICATOR 


coiMGOcooocot^i— iiooicot^OTrtr^ococooo 


cOOOt^i—  ( 


'—  i^oao(Niooo(Nioooi—  iiooO'—  1^0001—  i 


00   Tt<   O5   "*<   O5 

co  o  co  b-  o 


Tfir^O"*i^ococo 
oooooiooiooo 


o  o  co  t^  o 


§§§8§S 


t^t^rt<T-iOOi—  lO^Ot^COOOCOCO^Ot^OO-^rHOOC^'OCOTHOCOiOI^ 
i—  iCOi—  liOCOOr^OOOOi—  (<MCDt^COCOCOC5Ci-^CO(MI^-LOt^<MOOrHO> 
t^i-IOiCOiO^OifN^^OCOOiOOT^iOT^COCMOcOi—  1  I>  r-  Ir^iOQOO 


S 


oooooooooooooooooooooooooo 


<N<Nc3cs»<N<NC^<NC^COCO 


STEAM   CONSUMPTION   FROM  THE   DIAGRAM 


133 


CI  ^  CO  X  CO  CO  CO  CO  CO  CO  CO  X  CO  ^  Ol  CO  X  CD  ^ 


xcor^-cocito 

S6  g  §g  S  22  & 


CO  *O  t>-  Ci  <— iCO-fcOXCiOClCOtO 

i-HTft-^O'-Fr^OcOCOCiCOCOCiOl 


<M   30   -f   O 


XT^OCOiOl^Ci'— ICO 
t>-tOtOi— idt>-COOt>- 


X  01   CO  O  "*  X  CO  **  01  O  X 
t^  Ol  X  l~  t^  X  O  CO  CD  O  l^ 

l^Xt^-CDTtitoxCiOi— tO 


O  (N 


X  Ci  O  I-H  <N  CO 


5<*^    r— i    v.^    i.ij    ^p    «ij    i^»    jcj 
^  t^  O  CO  CO  Ci  C^  to 

t^t^r^xxxxciCi 


ci  o  x 

tO  to  CO 


T^     Tf     Tt<     Tt< 

CD  !M  OO  Tj< 

i— I    t^    rH    »O 


XOiM-^cOXOiM 
r^-i— i   CO  CO  iM  CO  I>-  M 

COClcOOCOtOCDt^- 


00  CO  t^  '-< 


1 

§ 


o  o  o  o  eo  co  eo  co  eo  co  oo  o  o  o  o  o  o'o  oooooxxxxxx 

tOiMt^OCiCOCOOt^n;'— lOWcOOlOOdCOOlOO'MCOcOCO'^OX 
COtOl~—XOi— id-^COt^-XO'— ("MCO^ 


o    co 


^  ;-J  ^ 


t>-   tO   CO  1-1 


i-H   CO    ^    CD   X 

O  CO  CD  c:  ^J 


'-HC^I^ftot^-XCiO'-HC^CO'^tOcOr—  XCi 
X'-"^t^.OCOCOOCOCOCi(MtooO'-(Tjit>. 

Oi  Ci 


X^Ot—  d^cOXOdTf" 
COr-Hi— (!McOX<MOCOCiCi 
CO  ^  ^*  CO  1"^  O  CO  tO  CO  CO  CO 


Cii-Hcotor>-xO'Mcotoccxci'-Hdcotocot>-xciOi— idco^fto 

OlCOCiC^tOXOJ'OX'— (•^t>-OTtit>.OCOcDCiOltoCi(MtOX'— 1^ 


<N  t^  to  CO  TH  Ci 
X  O  O  Ci  <N  X 
O  Ci  <N  CO  to  to 


X  O  <M  Ci  CO  !>•  i-H 


i— i  tO  Ci 

T-t  X  Ci 


^H  co  to  r^  x  c  01  ^  to 

o  01  to  x  ^H  to  ac  ^-1  Tt- 


oooocoooooo 

O1  *O  CO  ^O  Ol  ^^  CO  90  ^^  OJ  ^t^ 


XOi-HrHOOt^-Cli— (COCOTf^ 


CHAPTER   XVI 

DIAGRAMS   FROM   COMPOUND   ENGINES,   CLEARANCE 

NEGLECTED 

So  far  as  taking  the  diagrams  from  a  compound  engine,  figuring 
the  horse-power,  the  water  accounted  for,  etc.,  the  directions  already 
given  will  suffice.  The  diagram  will  be  taken  just  as  though  the  cylinder 
operated  upon  were  the  only  one  concerned,  the  selection  of  the  spring 
being  governed  by  the  range  of  pressures  in  that  cylinder  and  con- 
venience in  reducing  the  diagrams  to  a  common  scale,  as  will  be  explained. 
The  indicated  horse-power  is  found  by  computing  the  horse-power  of 
each  cylinder  in  the  ordinary  manner  from  its  own  diagrams  and  adding 
the  indicated  horse-power  of  the  several  cylinders  for  the  total  power 
of  the  engine.  The  steam  accounted  for  per  horse-power  per  hour  is 
obtained  by  referring  the  mean  effective  pressures  of  the  several  cylinders 
to  the  cylinder  in  which  the  pressure  used  for  the  computation  is  measured, 
as  explained  in  the  chapter  on  steam  consumption  from  the  diagram. 
Each  diagram  is  a  representation  of  the  distribution  and  use  of  steam 
in  the  conditions  of  its  own  cylinder,  and  may  be  studied  in  connection 
with  a  theoretical  diagram  for  these  conditions,  just  as  a  diagram  from 
a  single  cylinder  engine  would. 

In  order  to  study  the  action  of  the  steam  in  the  engine  as  a  whole, 
however,  and  to  compare  it  with  an  ideal  expansion  of  steam  through 
the  range  adopted,  the  diagrams  must  be  studied  in  their  relation  to  one 
another,  and  this  involves  their  reconstruction  in  several  particulars. 
In  the  first  place,  to  be  comparable,  the  diagrams  must  be  upon  the  same 
scale.  For  the  high  pressures  used  in  the  initial  cylinder  of  compound 
engines  a  stiff  spring  must  be  used.  In  order  to  get  a  large  diagram 
on  the  low-pressure  cylinder  a  spring  of  lower  scale  is  used.  When  we 
wish  to  compare  the  resulting  diagrams  we  must  reduce  them  to  the 
same  scale,  and  as  we  can  work  more  accurately  upon  a  large  than  a 
small  scale,  it  is  preferable  to  increase  the  height  of  the  high-pressure 
diagram  to  that  which  it  would  have  been  if  taken  with  the  same  spring 
as  the  other. 

Suppose  we  have  a  compound  engine  with  the  low-pressure  cylinder 
twice  the  diameter  of  the  high,  cutting  off  at  a  quarter  stroke  in  both 
cylinders,  with  a  boiler  pressure  of  160  pounds  absolute  and  26  inches 

134 


DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  NEGLECTED     135 


of  vacuum,  the  stroke  of  both  cylinders  being  equal;  and  that  from 
this  engine  we  had  got  the  diagrams,  Fig.  112,  with  an  80  scale,  and 
Fig.  113,  with  a  20  scale.  ;  Neglecting  for  the  present  the  influence  of 
clearance,  let  us  combine  them  so  as  to  show  the  continuous  action  of 
the  steam  in  the  whole  engine. 

If  the  high-pressure  diagram  had  been   taken  with   a  20  instead  of 
an  80  spring  every  point  upon  it  would  have  been  £g-=4  times  as  high 

above    the    atmospheric    line    as    the    diagram 
shows  it.     The  first  step,  therefore,   is  to   re- 
draw this  diagram  four  times  its  present  height. 
Divide  the   diagram   into   a   convenient 
number     of    equal    parts    and    erec 


\ 


High 


Pres 


SCAL 


•      X      1 


10 


13 


FIG.  112. 


15  16 

etr.N.T. 


ordinates  upon  the  divisions.  In  Fig.  112  sixteen  spaces  have  been 
used,  as  they  are  easily  obtained  by  successive  halvings;  or  the  spacing 
may  be  done  by  using  the  scale  diagonally  across  the  diagram,  as  in 
Fig.  74.  Measure  the  distances  from  the  atmospheric  line  to  the  forward- 
and  backward-pressure  lines  of  the  diagram  on  each  ordinate,  and  transfer 

these  distances,  multiplied  by  four,  to  the  cor- 
responding ordinate  upon  the  larger  diagram. 
On   ordinate   8,  for   example,  the   distances 
A B  and  AC  in   Fig.  114  are  four   times 
the  distances  ab  and  ac  on  the  cor- 


Low  Pressure 


20  SCALE 


FIG.  113. 
i 

responding  ordinate  in  Fig.  112.  A  pair  of  proportional  dividers  will  be 
found  convenient  for  this  work.  Drawing  a  line  through  the  points  thus 
indicated,  we  obtain  the  diagram  shown  in  Fig.  114.  AVhere  sudden 
changes  of  pressure  occur,  so  that  it  would  be  difficult  to  draw  the  line 
correctly  between  points  so  far  apart,  additional  ordinates  may  be  put 


136 


THE   STEAM   ENGINE   INDICATOR 


"~—  -~^ 

4^          in,  as    at  x,  Fig.  112,  putting  an  ordinate  in  th 

\ 

X 

\ 

same  position  on  the  reconstructed  diagram. 

\              We  can  now  consider  the  diagrams 

somewha 

1         in    their    relation    one    to    another    by    placin 

\         them  together,  as  shown  in 

Fig. 

114 

,  where  t 

\          the  low-pressure    diagram 

is  just 

as    it   wa 

\            drawn  by  the   indicator. 

The 

steam   is   e* 

\             panded  to  about  40   pounds, 

exhausts   int 

\ 

the  receiver,  and    the    space   between   th 

\ 

back-pressure    line    of 

the 

high-pressui 

\l               diagram  and  the  steam  line  of 

the 

lo\\ 

1 

pressure  shows  the  loss  in 

going  throug 

i 
i 

the  ports  and  receiver  between  the  tw 

i 
i 
k 

cylinders. 

But  even  now  we  are  not  able  to  corr 

\pare  the  diagrams 

with  a 

theoretics 

i 

diagram  showing  the  expansion 

of  th 

1 

steam  from  the  initial 

pressure  to  th 

, 

terminal  in  the 

low-pressure 

cylir 

\ 

\ 

\        der.     To   do  this  they  must 

be  re 

\ 

\       duced  to  the  same  scale  of  volume 

V 

c 

If  the  area  of   the  hi^ 

;h-pressui 

\ 

\       piston    was 

one    square 

foo 

\ 

then  every 

foot  of 

movemer 

\ 

\     of  that  piston  would  expan 

I 

1 

\ 

the 

steam 

behind 

\ 

Si 

one   cubic 

foo 

\ 

\ 

sxs 

x 

\ 

\ 

\ 

I    \ 

\ 

e 

~\ 

E 

H, 

v^_ 

d 

B 

^^ 

/ 

/ 

^: 

_--•' 

^^. 

^ 

A 

FIG.  114. 


DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  NEGLECTED      137 


If  the  low-pressure  piston  has  twice  the  diameter  of  the  high 
it  would  have  four  times  the  area,  and  each  foot  of  movement 
of  the  low-pressure  piston  would  add  four  cubic  feet  to  the 
volume  of  the  steam.  One  foot  of  movement  of  the  low- 
pressure  piston  is  equal,  then,  to  four  feet  of  the  high;  and 
since  the  movement  of  the  piston  is  represented  by  the  length 
of  the  diagram,  the  high-pressure  diagram,  to  be  comparable 
to  the  low,  should  be  only  one-fourth  the  length  of  the  low- 
pressure  diagram. 

This  calculation  has  been  made  on  the  assumption  that 
the  larger  cylinder  had  twice  the  diameter  of  the  smaller  and 
that  the  strokes  were  equal.  In  general  the  diagrams  should 
be  to  each  other  in  length  as  the  volumes  of  their  respective 
cylinders.  The  volume  of  the  cylinder  (clearance  neglected) 
is  the  cross-sectional  area  multiplied  by  the  length  of  the 
stroke;  the  area  is  the  square  of  the  diameter  multiplied  by 
0.7854.  Then  letting 

d=  diameter  high-pressure  cylinder; 
D=  low-pressure  cylinder; 

/  =  length  stroke  high-pressure  cylinder; 
L=  low-pressure  cylinder; 

the  ratio  of  the  lengths  of  the  diagrams  would  be 

d2X  0.7854  Xl 
D2X  0.7854  XL' 


The  decimals  cancel,  and  as  the  stroke  is  ordinarily  the 
same  in  both  cylinders  the  lengths  usually  cancel  also,  so 
that  usually  the  ratio  of  the  diagram  length  is 


In  our  case  we  found  this  ratio  to  be  J,  that  is, 
the  high-pressure  diagram  must  be  \  as  long  as 
the  low. 

Lay  off  on  the  admission  end  of  the 
enlarged  diagram,  Fig.  114,  a  length 

^s, 

ATMOSPHERIC 


ABSOLUTE  ZERO 

FIG.  115. 


138  THE  STEAM   ENGINE   INDICATOR 

equal  to  J-  the  length  of  the  low-pressure  diagram,  divide  it  int< 
as  many  spaces  as  the  original  diagram  was  at  first  divided,  16  ii 
this  case,  and  erect  ordiriates  as  shown.  Then  transfer  the  pressure; 
on  the  ordinates  of  the  large  diagram  to  the  corresponding  ordinate; 
of  what  will  be  the  shortened  diagram.  For  instance,  we  made  a  do 
d  on  the  last  ordinate  of  the  shortened  diagram  at  the  same  height  ai 
the  point  D,  where  the  line  touches  the  last  ordinate  of  the  large  diagram 
another  at  e  on  the  second  ordinate;  counting  from  the  right,  at  the  sami 
height  as  E  on  the  corresponding  ordinate  of  the  large  diagram;  am 
so  on  for  both  the  forward  and  back  pressure  lines  upon  all  the  sixteei 
ordinates.  Connecting  these  points  we  get  the  diagram  shown  by  thi 
dotted  line,  as  though  it  had  been  taken  with  a  20  spring  and  only  one 
quarter  the  movement  to  the  paper  barrel  that  the  low-pressure  diagran 
had.  If  this  diagram  is  placed  above  the  low-pressure  diagram,  as  ii 
Fig.  115,  we  have  a  representation  of  the  continuous  action  of  the  stean 
and  can  draw  about  it  the  theoretical  diagram,  as  shown  by  the  dotte( 
line,  showing  how  much  of  the  inclosed  area  is  covered  by  the  diagram; 
from  the  engine,  and  how  nearly  perfect  the  utilization  of  the  stean 
has  been. 


CHAPTER   XVII 


DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE 
CONSIDERED 

IN  the  last  chapter  was  described  the  combination  of  diagrams  from 
the  various  cylinders  of  a  compound  engine  so  as  to  be  comparable  with 
an    equivalent    action    of    the    steam    in    a    single    cylinder. 
Clearance  was   neglected  for  the  sake  of    simplicity,  but  it 
now  becomes  necessary  to  proceed  to  the  consideration   of 
the  effect  of  clearance  in  such  a  combination.     Its  treat- 
ment is  shown  in  Fig.   116  for   a   two-cylinder   engine  in 
which  the  diameters  of  the  cylinders  are  as  2  to  1,  making 
the  volumes   for   equal    strokes  as  4  to  1.     In  the  low- 
pressure  cylinder  the  clearance  is  -fa,  or  8J  per  cent  of 
the  displacement.     Draw  the  line  of  zero  pressure,  per- 
fect vacuum  OX,  Fig.  116,  and  at  a  distance  ab  (=-^3- 
the  length  of  the  low-pressure  diagram)  from  the  ad- 
mission line  erect  the  line  OA  of  zero  volume.     Then 
set  the  reconstructed  high-pressure  diagram  at  such  a 
distance  from  the  line  OA  that  the  clearance  space  cd 
shall  be  the  proper  percentage  of  the  length  de  of  that 
diagram.     In  other  words,  add  the  clearance  line  in  the 
usual  manner  to  the  reconstructed  diagrams,   and  in 
combining  make  the  clearance  lines  coincide. 
Let  us  consider  a  little  further  the  action  of  steam 
in  compound  engines,    using   for  the  purpose  con- 
ventional  or   theoretical   diagrams   drawn  upon 

the  same  scales 
for  both  cylin- 
ders. Let  us 
take  first  the  en- 
gine with  no  re- 
ceiver but  with 
the  high-pressure 

exhausting  directly  into  the  low,  and  the  pistons  moving  together,  as  in  a 
tandem,  or  with  equal  opposite  movements,  as  with  a  cross-compound  the 
cranks  of  which  are  opposite.  Suppose  the  cut-off  to  take  place  in  the 

139 


FIG.  116. 


140 


THE   STEAM  ENGINE   INDICATOR 


high-pressure  cylinder  at  one-quarter  stroke,  C,  Fig.  117,  in  which  case 
the  steam  would  be  expanded  to  the  terminal  pressure  T,  say  30  pounds. 
Now  suppose  a  valve  as  at  A,  Fig.  118,  between  the  two  cylinders,  to  open, 
and  the  pistons  to  commence  to  move  toward  the  left.  As  the  area  of 
the  low-pressure  cylinder  is  four  times  as  great  as  that  of  the  high,  every 
inch  of  movement  will  add  four  times  the  volume  in  the  low-pressure 
cylinder  that  is  taken  up  by  the  forward  movement  of  the  high-pressure 
piston.  When,  for  instance,  the  pistons  have  made  one-quarter  of  their 


c\     c\ 


- 


FIG.  117. 


stroke,  and  are  in  the  position  shown,  the  steam  will  still  have  three- 
quarters  as  much  room  to  occupy  in  the  high-pressure  cylinder  as  it 
had  before  the  return  stroke  was  commenced,  and  in  addition  it  will 
have  one-quarter  of  the  low-pressure  cylinder.  As  the  low-pressure 
has  four  times  the  volume  of  the  high,  the  steam  will  have  in  one-quarter 
of  the  low-pressure  as  much  room  as  it  had  in  the  high-pressure  cylinder 
at  the  end  of  the  forward  stroke,  besides  the  three-quarters  of  its  original 
volume,  still  left  in  the  high-pressure  cylinder.  Its  volume  has,  there- 
fore, at  the  point  under  consideration,  been  expanded  to  If  that  at  the 


DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  CONSIDERED    141 


termination  of  the  forward  stroke,  and  knowing  that  the  pressure  is  in- 
versely as  the  volume  (see  Chapter  on  Expansion  Line),  we  divide  the 
terminal  pressure  30,  by  If,  and  find  a  little  over  17  pounds  as  the  pres- 
sure at  the  point  e,  Fig.  117.  Locating  the  pressure  at  the  other  points 
in  the  same  manner,  we  find  that  the  back  pressure  on  the  high-pressure 
piston,  which  in  this  case  would  also  be  the  forward-pressure  on  the  low- 


FIG.  118. 

pressure,  would  follow  the  line  TA,  Fig.  120,  with  an  uninterrupted  pas- 
sage of  the  steam  between  the  cylinders  throughout  the  stroke. 

If  the  point  of  cut-off  in  the  high-pressure  cylinder  were  to  change, 
it  would  change  the  terminal  pressure  T  in  that  cylinder,  and  correspond- 
ingly increase  or  diminish  the  initial  pressure  in  the  low.  Instead  of 
cutting  off  at  (7,  Fig.  117,  one-quarter  of  the  stroke,  the  steam  were  cut 


Low  Pressure 
1  Vol. 


FIG.  119. 

off  at  c,  one-third  of  the  stroke,  the  terminal  pressure  would  be  t  instead 
of  T,  and  the  back-pressure  line  of  the  high-pressure  diagram,  which  is 
at  the  same  time  the  steam  line  of  the  low-pressure  diagram,  would  be 
ta.  If,  on  the  other  hand,  the  cut-off  is  earlier  in  the  high-pressure, 
the  initial  for  the  low-pressure  will  be  lowered  and  less  work  will  be  done 
in  that  cylinder. 


142 


THE   STEAM   ENGINE   INDICATOR 


Now  suppose  that  instead  of  remaining  open,  the  valve  A,  Fig.  118, 
between  the  cylinders,  closed  at  quarter  stroke,  giving  a  one-quarter 
cut-off  in  the  low-pressure  cylinder  as  well  as  in  the  high.  This  would 
carry  the  expansion  line  of  the  low-pressure  along  the  line  eE,  but  it 
would  shut  up  the  exhaust  of  the  high-pressure  cylinder,  and  compres- 
sion would  commence  at  e,  running  the  back-pressure  line  rapidly  up 
in  the  direction  ef. 

Now  suppose  that  instead  of  exhausting  directly  into  the  low-pressure 


FIG.  120. 

cylinder  the  high-pressure  exhausts  into  a  receiver  or  reservoir,   from 
which  the  low-pressure  takes  its  supply,  as  in  Fig.  119. 

This  receiver  can  be  so  large  in  proportion  to  the  cylinders  that  the 
fluctuations  in  the  quantity  of  steam  taken  from  and  delivered  to  it 
during  the  stroke  will  affect  the  pressure  but  little.  Understand  that 
the  low-pressure  cylinder  must  take  out  of  the  receiver  as  much  steam 
as  the  high-pressure  delivers  to  it.  It  is  obvious  that  it  cannot  con- 
tinuously take  out  more  and  if  it  does  hot  take  out  as  much  the  steam 
would  accumulate  in  the  receiver  and  raise  the  pressure  until  the  volume 


DIAGRAMS  FROM  COMPOUND  ENGINES,  CLEARANCE  CONSIDERED    143 

taken  by  the  low-pressure  contained  as  much  steam  as  the  high-pressure 
was  delivering.  Suppose  the  capacity  of  the  receiver  to  be  ten  times 
that  of  the  high-pressure  cylinder.  At  the  beginning  of  the  stroke  there 
will  be  one  volume  in  the  high-pressure  cylinder  and  ten  volumes  in  the 
receiver  of  steam  at  the  terminal  pressure  y=30  pounds,  11  volumes 
in  all.  At  quarter  stroke,  Fig.  118,  there  will  be  three-quarters  of  a  volume 
in  the  high-pressure,  ten  volumes  in  the  receiver,  and  one  volume  in  the 
low,  one-quarter  of  the  low-pressure  cylinder  being  equal  to  the  whole 


FIG.  121. 


volume  of  the  high,  llf  volumes  in  all.     The  pressure  will  have  fallen- 
then  to  only  TT-~  of  the  original  30,  or  to  a  little  over  28  pounds,  as  at 
1 1 .  /o 

g,  Fig.  120,  instead  of  to  17,  as  at  e,  Fig.  117.  Suppose  now  the  valve 
A,  Fig.  118,  to  close,  i.e.,  cut-off  to  occur  on  the  low-pressure  cylinder. 
The  expansion  in  that  cylinder  would  follow  the  line  gh,  Fig.  120,  while 
the  high-pressure  cylinder  would  continue  to  exhaust  into  the  receiver, 
and  at  the  end  of  the  stroke  would  have  taken  back  that  excess  of  three- 
quarters  of  a  volume  which  it  had  when  cut-off  occurred  on  the  low- 


144  THE  STEAM  ENGINE   INDICATOR 

pressure,  and  brought  the  pressure  back  from  28  to  30  pounds,  the  coun- 
ter-pressure following  the  line  gi. 

Suppose  a  heavier  load  to  come  on  the  engine,  changing  the  point 
of  cut-off  from  one-quarter  to  one-third  stroke.  First  let  us  consider 
the  effect  with  a  fixed  cut-off  on  the  low-pressure  cylinder,  which  we 
will  allow  to  remain  at  one-quarter  stroke.  The.  result  is  shown  by  the 
dotted  diagram  in  Fig.  120.  The  greater  portion  of  the  increase  of  load 
is  taken  by  the  low-pressure  cylinder,  on  which  the  cut-off  has  not  changed, 
the  area  gained  by  the  later  cut-off  in  the  high-pressure  cylinder  being 
largely  offset  by  the  loss  of  area  due  to  the  increase  of  back  pressure 
through  the  higher  terminal.  Notice  also  that  with  the  low-pressure 
cut-off  set  at  one-quarter,  the  volume  which  the  low-pressure  cylinder 
takes  out  of  the  receiver  each  stroke  just  equals  the  volume  delivered 
to  it  by  the  high-pressure,  so  that  whatever  the  terminal  pressure,  the 
high-pressure  diagram  will  end  in  a  point. 

Suppose  now  there  had  been  an  automatic  cut-off  on  both  cylinders, 
and  that  the  low-pressure  cut-off  changed  to  one-third  stroke  too.  The 
low-pressure  cylinder  has  four  times  the  volume  of  the  high.  One-third 
of  the  low  would  have  JX4  =  1J  times  the  volume  of  the  high,  so  that 
for  every  cubic  foot  of  steam  that  the  high-pressure  cylinder  delivers 
to  the  receiver  the  low-pressure  cylinder  takes  out  1J  cubic  feet.  Since 
there  is  a  greater  volume  going  out  of  the  receiver  than  there  is  going 
into  it,  the  pressure  will  fall  until  the  greater  volume  taken  out  by  the 
low-pressure  cylinder  contains  only  the  same  quantity  or  weight  of 
steam  as  that  delivered  in  a  smaller  volume  by  the  high-pressure  cylin- 
der. In  other  words,  the  receiver  pressure  will  fall  until  the  cylinderful 
of  steam  delivered  to  the  receiver  at  40  pounds  will  expand  to  1J  times 
its  volume  in  the  receiver,  which  should  require  a  receiver  pressure  of 
40  -r- 1^=30  pounds.  We  should  therefore  have  a  diagram  like  Fig.  121, 
where  the  dotted  lines  represent  both  cylinders  cutting  off  at  one-quarter 
stroke,  the  full  lines,  both  cylinders  cutting  off  at  one-third  stroke. 


CHAPTER   XVIII 
ERRORS   IX   THE   DIAGRAM 

IN  treating  of  the  reducing  motion  we  have  described  in  kind  the 
various  errors  to  which  it  is  liable.  It  now  remains  to  consider  them 
in  degree.  Fig.  122  shows  the  error  which  would  result  from  taking 


\ 


FIG.  122. 

the  motion  from  a  pin  on  a  lever  like  Fig.  123,  vibrating  through  about 
90°.  A  diagram  which  should  follow  the  full  line  would  be  distorted 
by  this  arrangement  to  that  shown  by  the  dotted  lines.  The  cut-off 
would  appear  too  early,  the  expansion  line  would  hold  up  too  much  for 
the  apparent  cut-off,  but  would  be  below  its  proper  position  in  the  first 
of  the  stroke,  crossing  the  correct  line  at  the  center,  and  making  the  ter- 
minal appear  higher  than  it  should  be.  It  makes  the  release  and  com- 
pression appear  late  and  reduces  the  area  of  the  diagram,  and  hence 
the  apparent  indicated  horse-power.  Both  the  right-  and  left-handed 
diagrams,  i.e.,  those  from  the  head  and  the  crank  end,  are  affected  the 
same  way.  When  you  see  a  diagram  which  resembles  the  dotted  one 
in  Fig.  122,  look  over  the  reducing  motion. 

145 


146 


THE   STEAM  ENGINE   INDICATOR 


As  just  stated,  Fig.  122  was  drawn  upon  the  assumption  that  tin 
lever  vibrated  through  90°.  This  is  excessive.  It  is  recommended  t< 
use  a  lever  not  less  than  one  and  a  half  times  the  length  of  the  stroke 
This  gives  a  vibration  between  35°  and  40°.  In  Fig.  124  is  shown  th< 
distortion  due  to  using  a  lever  like  Fig.  123,  one  and  a  half  times  th< 
length  of  the  stroke,  taking  the  motion  from  a  pin  in  the  lever,  and  { 
cord  led  off  parallel  to  the  guides. 

The  distortion  is  much  less  than  with  the  shorter  lever,  and  th< 
purpose  for  which  the  diagram  is  taken  must  determine  whether  thi 
amount  can  be  tolerated  for  the  sake  of  simplicity  in  the  reducing 
motion.  When  we  measure  for  a  carpet  we  do  not  take  into  accoun 


FIG.  124. 

the  fractions  of  an  inch,  and  when  we  weigh  coal  we  do  not  pay  atten 
tion  to  the  ounces.  In  ordinary  indicating  to  see  that  the  valve  gea 
has  not  become  deranged,  to  make  a  rough  cast  of  the  power  for  pur 
poses  of  record,  etc.,  we  need  not  be  so  precise  as  though  we  were  testing 
a  cruiser,  when  the  difference  of  one  pound  mean  effective  pressure  wouh 
mean  ten  thousand  dollars  to  the  builders;  or  a  steam  plant  where  i 
few  horse-power  more  or  less  would  determine  for  or  against  the  guar 
antee;  or  when  with  Hirn,  we  undertake  to  trace  from  the  diagran 
the  distribution  and  disposition  of  the  heat  units  going  through  the 
plant.  This  is  when  the  indicator  and  its  user  must  get  right  dowr 
to  extreme  accuracy,  and  after  every  precaution  is  used  the  results  wil 
still  be  too  far  from  the  truth.  This  motion  cannot  be  corrected  b} 


ERRORS  IN  THE   DIAGRAM 


147 


the  use  of  a  brumbo  pulley,  for  the  pulley  would  not  move  through  equal 
arcs  for  equal  movements  of  the  cross-head.  It  would  pull  the  cylinder 
a  distance  equal  to  4',  5',  Fig.  122,  in  the  middle  of  the  stroke,  and 
only  that  equal  to  1',  2',  etc.,  at  the  ends,  so  that  instead  of  being 
equally  divided  for  equal  movements  of  the  piston  the  diagram  would 
be  divided  irregularly,  as  are  the  spaces  on  the  arc.  If  this  arc  were 
straightened  out,  reduced  to  the  length  of  the  diagram  without  dis- 
turbing the  proportion  of  the  spacing,  corresponding  ordinates,  as  3'/, 
erected,  and  the  pressure  transferred  to  these  from  the  proper  ordinates, 
as  from  B  to  /,  we  should  get  the  diagram  represented  by  the  broken 


FIG.  125. 

line,  showing  that  the  use  of  the  arc  is  productive  of  greater  accuracy 
in  this  case.  With  a  lever  of  constant  length,  as  in  Fig.  125,  however, 
the  use  of  the  arc  introduces  an  error.  (See  chapter  on  reducing 
motions.) 

Leading  the  cord  away  from  the  reducing  motion  in  any  other  direc- 
tion than  parallel  with  the  guides  introduces  an  error.  Let  us  see  how 
much.  Suppose  we  have  a  pantograph,  as  in  Fig.  126,  or  a  reducing 
wheel,  as  in  Fig.  127,  and  that  instead  of  leading  the  cord  off  in  the 
direction  AB  parallel  with  the  guides,  we  led  it  off  in  the  direction  shown, 
the  angle  being  30°  when  the  cross-head  is  nearest  to  the  cylinder. 


148 


THE   STEAM   ENGINE   INDICATOR 


The  resulting  distortion  of  the  diagram  will  be  that  shown  in  Fig.  128. 
When  the  piston  has  traveled  one-eighth  of  its  stroke  the  pencil,  which 
should  be  at  A,  will  be  a,  and  so  on  for  the  other  ordinates.  Notice 
that  this  makes  the  apparent  cut-off  earlier  on  the  head-end  and  later 
on  the  crank-end.  At  all  times  and  in  both  directions  the  travel  of 
the  paper-drum  is  less  than  it  should  be,  altogether  it  looks  to  be  more 
when  traveling  to  the  right.  Thus,  starting  with  0  at  the  right  the 
pin  on  the  pantograph,  when  the  engine  cuts  off  at  quarter  stroke,  will 
have  moved  a  distance  equal  to  02,  but  the  movement  of  the  paperr 
drum  will  be  equal  to  OC  only.  When  the  stroke  is  completed  the 
pantograph  pin  has  traveled  through  a  distance  equal  to  08,  but  the 
paper-drum  has  traveled  through  OD,  the  comparative  movement  of 
the  pantograph  pin  and  the  paper-drum  for  successive  eighths  of  fche 


FIG.  126. 


stroke,  being  shown  by  the  bold-faced  figures  1,  2,  3,  etc.,  and  the  dotted 
ordinates  to  the  right  of  them.  The  full-line  ordinates  are  placed  upon 
the  equal  eighths  of  the  shortened  diagram  OD.  Starting  at  D  back- 
ward the  pantograph  pin  would  move  in  the  first  eighth  of  the  stroke 
to  1,  in  the  second  eighth  to  2,  etc.  The  corresponding  position  of  the 
pencil  on  the  paper  would  be  at  the  dotted  ordinates  as  before,  a  less 
distance,  it  will  be  seen,  than  the  actual  movement  in  every  case;  but 
when  we  come  to  erect  the  full-line  ordinates  on  the  even  eighths  of  the 
shortened  diagram  they  fall  behind  the  dotted  lines,  showing  how  we 
can  get  an  apparently  excessive  movement  on  the  crank  end  with  a 
movement  really  less  than  it  should  be.  Notice  that  the  distortion  due 
to  this  cause  tends  to  throw  the  card  out  of  balance,  affecting  the  dia- 


ERRORS   IN  THE   DIAGRAM 


149 


grams  from  the  head-  and  crank-ends  in  different  directions,  not  in  the 
same  way  as  did  the  distortion  of  the  lever  motion  in  Fig.  122. 

Another  source  of  error  in  the  diagram,  briefly  referred  to  before,  is 
that  due  to  a  long  and  indirect  passage  from  the  cylinder  to  the  indicator. 
The  errors  introduced  are:  less  realized  pressure,  lower  compression 
and  higher  terminal.  This  subject  has  been  discussed  in  the  various 
technical  papers,  and  varying  opinions  have  been  elicited.  In  order 
to  determine  this  question,  the  author,  in  connection  with  Mr.  A.  C. 
Lippincott,  undertook  the  tests  resulting  in  the  diagrams  shown  in  Figs. 
129  to  138.  We  designed  the  apparatus  shown  in  Fig.  129. 

A  a 


Crank 


End 


Head  End 


SCc  6 


FIG.  128. 


rr,  A".  JT. 


Our  first  test  was  made  on  an  11X11  Ball  &  Wood  engine  at  the 
Roosevelt  Building,  New  York,  through  the  courtesy  of  Mr.  Thomas 
Murphy,  the  engineer  in  charge.  The  engine  was  running  at  270  revolu- 
tions per  minute,  driving  an  electric  generator  with  a  very  constant  load, 
so  constant  that  when  the  pencil  was  held  on  for  20  revolutions  the  line 
of  the  diagram  was  scarcely  thickened.  Three  and  a  half  feet  of  half- 
inch  pipe  connected  the  cross  F  with  the  tee  G,  and  a  similar  length  was 
used  between  E  and  HJ  the  right  and  left  nipple  I  being  about  7  inches 
long.  This  pipe  was  thoroughly  heated  and  drained  before  each  card 
was  taken,  by  turning  the  three-way  cock,  so  that  steam  could  issue 


150 


THE   STEAM   ENGINE   INDICATOR 


through  the  little  escape  orifice,  opening  the  drips  and  the  cock  B,  the 
engine  running  continuously. 

Having  taken  a  diagram  with  the  direct  connection,  the  three-way 
cock  was  reversed  and  the  cock  B  opened,  compelling  the  steam  to  travel 
through  the  loop  of  about  8  feet  of  |-inch  pipe  and  fittings  to  the  indicator. 
The  result  is  shown  in  Fig.  130.  The  pencil  was  allowed  to  pass  over 
the  card  20  revolutions  as  before,  to  insure  that  the  diagram  was  not 
erratic  or  exceptional.  This  experiment  was  repeated  over  and  over 
again.  Whenever  we  switched  to  the  direct  connection  we  got  Fig. 


To  Cylinde 


FIG.  129. 

131,  whenever  with  the  direct  connection  we  opened  the  connection  to 
the  piping,  we  got  Fig.  132;  and  when  the  steam  was  compelled  to  pass 
around  to  the  further  side  of  the  three-way  cock  to  get  to  the  indicator 
we  got  Fig.  130.  The  passages  through  the  pipes  and  fittings  were 
perfectly  clear,  and  ordinary  |-inch  plug  cocks,  half-inch  fittings  and  the 
three-way  cock  regularly  supplied  with  the  indicator  were  used.  The 
nipple  A  is  screwed  into  the  hole  in  the  cylinder  ordinarily  provided 
for  the  indicator  cock.  When  the  handle  of  the  three-way  cock  is 


ERRORS   IX  THE   DIAGRAM 


151 


thrown  to  the  right,  as  in  the  drawing,  the  steam  enters  the  cock  from 
the  left  and  has  a  direct  passage  to  the  indicator,  and  if  the  plug  cock 


FIG.  130. 


FIG.  131. 


FIG.  132. 


B  is  closed  the  steam  has  no  access  to  the  extraneous  piping,  and  the 
indicator  is  about  as  directly  connected  as  it  would  be  with  the  usual 


152 


THE   STEAM   ENGINE   INDICATOR 


nipple  elbow  and  single  cock.  The  plug  cock  C  is  open  and  D  is  closed, 
so  that  when  B  is  opened  steam  can  pass  clear  around  the  loop  and  enter 
the  three-way  cock  at  the  right,  as  it  must  do  to  get  to  the  indicator 
when  the  handle  of  the  three-way  cock  is  swung  the  other  way.  Any 
sort  of  a  circuit  of  piping,  steam  hose,  or  fittings  may  be  connected  at 
EF  for  the  steam  to  pass  through  on  its  way  to  the  indicator.  The  handle 
of  the  three-way  cock  can  also  be  left  so  as  to  give  the  steam  a  direct 
passage  to  the  indicator  and  the  cock  B  left  open  so  as  to  obtain  the 
effect  of  the  addition  to  the  clearance  without  the  friction  of  the 
pipe. 

Fig.  129  shows  the  apparatus  as  applied  to  a  cylinder  tapped  at  the 
side  as  are  engines  of  the  Corliss  type.     For  engines  tapped  on  top  of 


FIG.  133. 

the  cylinder  it  is  turned  as  shown  in  Fig.  133,  which  will  explain  the 
necessity  of  the  cocks  C  and  D. 

Fig.  134  is  a  card  on  which  all  three  diagrams  were  taken  as  quickly 
as  the  cocks  could  be  shifted.  Through  the  kindness  of  Mr.  Gillespie, 
in  charge  of  the  steam  plant  of  the  Young  Women's  Christian  Associa- 
tion Building,  we  were  able  to  repeat  the  experiment  on  a  12X12  New 
York  Safety  engine,  which  also  ran  at  270  revolutions,  but  was  more 
heavily  loaded.  This  load  was  also  electrical  and  very  steady,  Fig. 
135  being  its  diagram  with  the  direct  connection  and  35  passages  of  the 
pencil. 

Fig.  136  shows  very  prettily  the  effect  of  added  clearance  obtained 
by  opening  the  cock  B,  leaving  the  passage  to  the  indicator  still  direct. 


ERRORS   IN  THE   DIAGRAM 


153 


Fig.  137  shows  the  diagram  obtained  with  the  indirect  connection, 
the  pencil  passing  25  times  over. 


Puwr,  K.T. 


FIG.  134. 


FIG.  135. 


FIG.  136. 

Fig.  138  shows  all  three  diagrams  on  the  same  card. 
Seven  or  eight  feet  of  pipe  is  of  course  excessive  for  an  indicator 
connection,  though  not  much  more  so  than  6  feet  of  steam  hose.     If 


154 


THE   STEAM   ENGINE   INDICATOR 


such  a  difference  as  this  exists  with  8  feet  there  should  be  a  visible  dif- 
ference with  4r|  feet,  or  even  with  the  ordinary  side  pipe  on  a  long  cylinder. 
Fig.  131  is  a  photographic  reproduction  of  the  diagram  obtained  from 
the  first  engine  with  the  direct  connection,  the  pencil  passing  over  it 


FIG.  137. 

fully  twenty  times.  A  new  card  was  placed  upon  the  paper-barrel  and 
another  diagram  taken  under  the  same  conditions  as  Fig.  131.  Then 
leaving  the  three-way  cock  so  that  the  steam  passed  directly  to  the  in- 
dicator, the  cock  B  was  opened,  adding  the  pipe  to  the  volume  of  the 


Power,  .y.,T» 


FIG.  138. 


clearance,  and  another  diagram  was  drawn  upon  the  same  card.  The 
result  is  shown  in  Fig.  132,  and  is  as  would  have  been  expected — less 
realized  pressure,  lower  compression,  and  higher  terminal.  For  greater 
distinctness,  we  have  dotted  the  line  of  the  first  diagram,  which  will 
be  seen  to  be  identical  with  Fig.  131. 


CHAPTER  XIX 
MEASURING  THE  CLEARANCE 

THE  clearance  of  a  steam  engine  includes  not  only  the  space  between 
the  piston  face  and  cylinder  head,  but  all  of  the  port  or  ports  up  to  the 
valve  face  when  the  engine  is  on  the  dead  center.  It  is  necessary  to 
know  its  amount  whenever  any  accurate  calculations  are  made  con- 
cerning the  action  of  the  steam.  It  is  usually  expressed  as  a  fraction  of 
the  volume  displaced  by  one  stroke  of  the  piston,  or  what  is  equivalent 
to  this,  a  percentage  of  the  length  of  the  stroke. 

Fig.  139  shows  a  single-valve  engine  with  the  steam  chest  at  the 
side  of  the  cylinder,  and  the  closely  shaded  portion  represents  the 


FIG.  139. 

clearance.     If  the  valve  and  piston  are  tight,  the  amount  of  the  clear- 
ance may  be  found  both  easily  and  accurately  as  follows: 

Put  the  engine  carefully  on  the  dead  center  in  the  usual  manner 
and  set  the  valve  so  that  it  covers  the  port,  blocking  it,  if  necessary, 
to  hold  it  up  against  the  seat.  Make  a  fine  mark  aa  on  the  cross-head 
and  guides. 

Remove  the  indicator  plug  P  and  pour  in  enough  water  to  fill  the 
clearance  space  up  to  the  under  face  F  of  the  plug,  which  is  the  highest 
point  of  the  clearance.  Measure  or  weigh  carefully  the  amount  of  water 
poured  in  and  make  a  note  of  it. 

155 


156 


THE   STEAM   ENGINE   INDICATOR 


Now  turn  the  engine  over  until  the  cross-head  has  moved  3  or  4 
inches  of  its  stroke  and  pour  in  a  second  quantity  of  water  exactly  equal 
to  that  required  to  fill  the  clearance  space.  Then  back  the  engine  up 
until  the  water  rises  again  to  the  original  level  F.  The  cross-head  and 
piston  will  now  be  in  the  position  shown  in  Fig.  140  and  the  shaded 
portion  will  be  filled  with  water.  Make  a  second  mark  b  on  the  guides 
opposite  the  mark  a  on  the  cross-head.  The  dotted  line  XY,  Fig.  140, 
represents  the  original  position  of  the  cross-head,  and  the  space  to  the 
right  of  it  will  be  that  occupied  by  the  second  quantity  of  water  and 
will  represent  a  volume  equal  to  the  clearance.  The  fraction  of  the 
stroke  occupied  by  this  equivalent  volume  will  be  the  distance  ab  on 
the  guides,  and  all  that  is  needed  to  find  the  clearance  in  decimal  parts 


s— 

!  A 

1     \       i 
i     \^  ^/ 

—  i  

3 

K 

) 

1 

FIG.  140. 


of  the  stroke  is  to  measure  in  inches  the  distance  ab  and  divide  it  by 
the  length  of  the  stroke  in  inches. 

For  instance,  if  in  an  engine  of  15  inches  stroke  the  distance  ab  was 


found  to  be  1&  inches  (1.1875),  the  clearance  would  be  _i__-   =0.0791 

lo 

or  7-j9^  per  cent  of  the  stroke. 

In  engines  of  the  Corliss  type,  however,  the  indicator  opening  is  not 
on  top  of  the  cylinder,  but  usually  at  the  side,  as  shown  in  Fig.  141. 
This  objection  can  be  overcome  by  screwing  into  the  indicator  elbow  a 
short,  vertical  piece  of  pipe  just  long  enough  to  bring  the  top  end  to 
the  level  of  the  valve  face  as  in  the  figure.  Then  pour  in  the  water  until 
it  overflows  the  top  end  of  this  pipe,  leaving  the  steam  valve  open  about 
as  for  lead  to  prevent  entrapping  air  at  the  highest  point.  If  this  air 
were  not  allowed  to  escape,  it  would  be  compressed  until  its  pressure 
equaled  the  slight  head  of  water  and  it  would  not  be  possible  to  fill  the 
entire  clearance  space  with  water. 


MEASURING   THE   CLEARANCE 


157 


The  distance  ab  on  the  guides  is  then  found  as  before  by  pouring 
in  a  second  quantity  of  water  and  bringing  it  to  the  original  level.  It 
is  well  to  note  here  that  if  the  second  pouring  is  exactly  equal  to  the 
first,  we  shall  have  put  in  too  much  by  the  quantity  contained  in  the 
short  piece  of  pipe  from  P  to  T,  Fig.  141.  This  amount  may  be  obtained 


FIG.  141. 


by  measurement  before  the  pipe  is  screwed  into  place  and  should  be 
deducted  from  the  second  pouring  in  order  to  correctly  locate  point  6, 
Fig.  142.  In  the  above  method,  it  is  not  necessary  to  measure  or  weigh 
the  quantity  of  water  in  any  particular  units;  a  mark  on  a  bucket,  any 


FIG.  142. 

known  number  of  canfuls  or  a  balancing  weight  of  unknown  value  will 
give  two  equal  quantities. 

If  a  vessel  graduated  in  U.  S.  liquid  measure,  i.e.,  quarts,  pints,  and 
gills,  be  used  to  measure  the  first  pouring,  the  second  operation,  by 
which  mark  b  was  located,  may  be  omitted  and  the  clearance  found  by 
a  simple  calculation. 


158  THE   STEAM  ENGINE   INDICATOR 

Suppose  it  required-  3  quarts  1  pint  and  2  gills  of  water  to  fill  the 
clearance  of  an  engine  15  inches  diameter  by  15  inches  stroke.  In  U.  S. 
liquid  measure 

4  gills      =1  pint 

2  pints    =  1  quart 

4  quarts  =  1  gallon 

Since  1  gallon  =231  cubic  inches, 

1  gill  =  7.22  cubic  inches 
1  pint  =28.88  cubic  inches 
1  quart  =57. 75  cubic  inches 

The  volume  of  the  clearance  is  then 

3  quartsX57.75  =  173.25 

1  pint     X  28.88=  28.88 

2  gills     X   7.22=   14.44 

Total  =216.57  cu.  in. 

The  cylinder  area  is  152X0.7854  =  176.71  square  inches,  and  thi 
piston  displacement  for  one  stroke  is  176.71X15=2650.7  cubic  inches 
Therefore  the  clearance  is  216.6-^2650.7=0.0817  or  8.17  per  cent  o 
the  stroke. 

P.]ven  if  the  measuring  apparatus  is  not  graduated  finer  than  pints 
it  is  possible  to  estimate  with  reasonable  accuracy  to  quarter  pints 
so  that  the  error  will  not  be  serious. 

There  is  another  good  way  to  find  the  clearance  without  locating 
point  6  on  the  guides:  it  requires  only  the  use  of  a  pair  of  avoirdupois 
scales,  such  as  grocers  use,  and  a  bucket  holding  two  or  more  time; 
the  water  required  to  fill  the  clearance. 

To  illustrate  more  clearly  we  will  work  out  an  example.  Fill  thi 
bucket  with  water  and  weigh  it  carefully;  let  us  assume  that  the  bucke 
and  water  weigh  20  pounds.  Now  fill  the  clearance  space  from  the  bucket 
taking  care  to  spill  none  of  the  water,  and  again  weigh  the  bucket  am 
the  remaining  water;  suppose  that  it  now  weighs  12  pounds  and  2  ounces 
It  has  then  required  20  pounds—  12  pounds  2  ounces  =7  pounds  14  ounce 
=  7-}£  or  7.88  pounds  of  water  to  fill  the  clearance  space.  The  volum< 
of  a  pound  of  water  at  the  temperature  of  the  usual  room  is  27.7. 

The  volume  of  the  clearance  is  7.88X27.7=218  cubic  inches.  Th 
percentage  of  clearance  is  then  found  as  before  by  dividing  the  clearance 
volume  by  the  product  of  the  piston  area  and  stroke,  i.e.,  by  the  pistoi 
displacement. 


MEASURING   THE   CLEARANCE 


159 


In  engines  having  indicator  openings  on  the  side,  a  correction  must 
be  made  for  the  short  piece  of  pipe,  as  previously  mentioned. 

We  now  have  three  methods  of  finding  clearance : 

1. — By  linear  measure,  using  two  equal  quantities  of  water. 

2. — By  liquid  measure. 

3. — By  weight. 

There  is  still  another  method,  which  is  as  simple  as  any;  it  is  shown 
in  Fig.  143.  A  bucket  or  other  vessel  is  suspended  above  the  cylinder 
and  a  constant  supply  of  water  is  furnished  it  by  means  of  a  hose  or  pipe. 
From  the  bottom  or  side  of  the  bucket  a  small  rubber  hose  or  J-inch 
pipe  leads  the  water  to  the  cylinder.  The  head  of  the  water  on  the  dis- 
charge end  of  the  small  pipe  must  be  kept  constant  either  by  regulating. 


Supply 


FIG.  143. 


the  supply  to  the  bucket  so  as  to  keep  the  water  level  constant,  or  bjr 
allowing  the  bucket  to  overflow  continually.  If  the  latter  is  done,  the 
overflowing  water  must  not  follow  along  the  small  pipe  and  so  get  into 
the  cylinder.  This  can  be  prevented  by  using  a  siphon  to  supply  the 
cylinder.  The  operation  is  as  follows:  Put  the  engine  on  the  dead  center 
and  note  the  time  in  seconds  required  to  fill  the  clearance  space.  Shut 
off  the  supply  to  the  cylinder  and  put  the  engine  on  the  other  center. 
Then  through  the  same  pipe  and  under  the  same  head  fill  the  entire 
cylinder  and  clearance  space  up  to  the  original  level,  noting  separately 
the  time  in  seconds  required  to  fill  the  cylinder. 

Since  the  quantity  of  water  flowing  through  a  constant  opening 
under  a  constant  head  is  exactly  proportional  to  the  time,  the  clearance- 
is  equal  to  the  first  period  of  flow  divided  by  the  second  period. 


160  THE   STEAM   ENGINE   INDICATOR 

For  example,  suppose  it  requires  1  minute  and  25  seconds  (85  seconds) 
to  fill  the  clearance  space  and  28  minutes  and  20  seconds  (1700  seconds) 

to  fill  the  cylinder.     The  clearance  is  then       '=0.05  or  five  per  cent 

of  the  stroke. 

The  smaller  the  supply  pipe  to  the  cylinder,  the  longer  it  will  take 
to  fill  the  clearance  space  and  the  less  the  percentage  of  error  in  obser- 
vation. 

Various  modifications  of  the  details  will  suggest  themselves  for 
vertical  engines,  locomotive  engines  and  others.  In  every  case  it  is 
important  to  leave  an  opening  for  the  escape  of  air  at  the  highest  point. 

Suppose  that  instead  of  having  plugs  in  the  indicator  openings  the 
engine  were  provided  with  a  j-inch  standard  indicator  pipe  and  3-way 
cock,  as  shown  by  the  dotted  lines  in  Fig.  139.  The  clearance  space 
would  then  include  that  portion  of  the  indicator  pipe  from  the  face  of 
the  3-way  cock  to  the  cylinder  connection.  For  a  15X15  inch  engine, 
this  additional  amount  would  be  about  11 J  inches  of  J-inch  standard 
pipe.  The  internal  area  or  this  pipe  is  0.53  of  a  square  inch,  and  the 
added  clearance  volume  due  to  it  is  0.53X11J=6.10  cubic  inches.  In 
finding  the  clearance  of  an  engine  equipped  thus,  the  water  should  be 
poured  in  through  the  indicator  connection  until  it  is  just  visible  from  the 
top.  When  the  side  pipe  is  used  and  it  is  necessary  to  use  a  riser  the 
contents  of  the  riser  must  be  found  separately  and  deducted. 

The  publication  of  the  foregoing  direction  for  measuring  clearance, 
prepared  by  Mr.  C.  G.  Robbi  s  of  the  editorial  department  of  Power, 
called  out  the  following  suggestion  from  Prof.  John  E.  Sweet: 

The  engine  valve  and  piston  must  be  made  tight  and  the  engine  set 
on  the  dead  center  as  in  any  case.  Set  upon  a  platform  or  counter  scale 
a  pail  of  water  and  an  empty  pail,  and  balance  them  by  the  weight  on 
the  scale.  Fill  the  clearance  space  from  the  pail  of  water,  and  then  from 
outside  source  put  enough  water  in  the  empty  pail  to  again  balance 
the  scale.  Mark  the  cross-head  and  guide,  turn  the  engine  forward 
a  little  way  and  put  the  water  in  the  second  pail  in  the  cylinder,  and  turn 
the  engine  back  until  the  water  comes  up  in  the  indicator  hole,  and  again 
mark  the  cross-head  as  was  clearly  explained  in  the  foregoing. 

In  the  case  of  a  Corliss  engine  where  a  stand  pipe  is  necessary  to 
fill  through  the  indicator  hole,  after  the  scale  has  been  balanced  with 
the  pail  of  water,  and  empty  pail  as  above  described,  take  off  the  stand 
pipe,  fill  it  with  water  and  put  it  in  the  pail  of  water,  then  after  putting 
on  the  stand  pipe  proceed  as  before. 

So  far  we  have  in  a  simple  way  obtained  two  marks  on  the  guide 
which  truly  represent  the  distance  the  piston  has  to  travel  to  equal 
the  clearance,  and  whether  the  result  is  in  even  inches,  which  would 


MEASURING  THE   CLEARANCE 


161 


render  it  simple  to  determine  the  per  cent,  or  in  fractions,  which  would 
complicate  the  problem,  the  following  graphic  method  answers  equally 
well,  and  is  readily  performed  by  anyone  who  can  use  a  rule. 

Draw  a  horizontal  line  as  in  Fig.  144,  and  lay  off  the  stroke  of  the 
engine  AB}  and  draw  the  vertical  line  from  B;  at  C  draw  another  vertical 
line  the  same  distance  from  A  as  the  two  lines  marked  on  the  guide. 
From  A  with  100  units  of  any  comvenient  length  measure  up  on  the 
line  #,  that  is  to  say,  if  the  stroke  of  the  engine  be  11  inches,  measure 
up  from  A  to  some  point  on  the  line  F  to  D  12J  inches,  which  is  a  hundred 


• — Length  of  Stroke - 

FIG.  144 


C  "deanncoJA. 


units  of  J  inch  each,  then  from  D  to  A  strike  the  straight  line  E  and  as 
many  J  inches  as  there  are  from  A  to  F,  so  much  will  be  the  per  cent 
of  clearance  in  the  engine.  If  the  stroke  of  the  engine  is  between  13 
and  18  inches,  18}  inches  may  be  used  for  the  line  E  when  ^  of  an  inch 
will  be  the  unit,  or  if  from  18  to  24  inches,  then  25  inches  for  the  line  X 
with  J  inch  as  a  unit  and  so  on. 

Of  course  this  is  not  the  mathematicians'  way  of  doing  things,  but 
it  eliminates  many  sources  of  error,  is  quick,  easy  to  understand,  and 
just  as  accurate  as  the  man  who  does  it  is  able  to  work,  and  that  is  the 
measure  of  accuracy  in  about  everything. 


TABLE  I.  — HYPERBOLIC   LOGARITHMS. 


X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

.OI 

•  00995 

1-57 

.45108 

2.13 

.75612 

2.69 

.98954 

.02 

.01980 

1.58 

•45742 

2.14 

.  76081 

2.70 

•99325 

•03 

.02956 

i.59 

•46373 

2.15 

•76547 

2.71 

•99695 

.04 

.03922 

i.  60 

.47000 

2.16 

.77011 

2.72 

.00063 

•05 

.04879 

1.61 

.47623 

2.17 

•77473 

2.73 

.00430 

.06 

.05827 

1.62 

.48243 

2.18 

•77932 

2.74 

.00796 

.07 

.06766 

1.63 

.48858 

2.19 

•  78390 

2.75 

.01160 

.08 

.07696 

1.64 

.49470 

2.20 

.  78846 

2.76 

•01523 

.09 

.08618 

1.65 

.50078 

2.21 

•  79299 

2.77 

.01885 

.IO 

•09531 

1.66 

.50681 

2.22 

•79751 

2.78 

.02245 

.11 
.12 

.  10436 
•II333 

i  68 

.51282 

2.23 
2.24 

.80200 
.80648 

I'K 

.02604 
.02962 

•13 

.  12222 

1.69 

•52473 

2.25 

•81093 

2.81 

•03318 

.14 

.13103 

1.70 

•53063 

2.26 

•81536 

2.82 

.03674 

.15 

•13977 

1.71 

•53649 

2.27 

.81978 

2.83 

.04028 

.16 

.14842 

1.72 

.54232 

2.28 

.82418 

2.84 

.04380 

.17 

.15700 

1-73 

.54812 

2.29 

•82855 

2.85 

.04732 

.18 

•16551 

1.74 

.55389 

2.30 

.83291 

2.86 

.05082 

.19 

•17395 

1.75 

•55962 

2.31 

•83725 

2.87 

•05431 

.20 

.18232 

1.76 

•56531 

2.32 

•84157 

2.88 

•°5779 

.21 

.  19062 

1-77 

•57098 

2-33 

-84587 

2.89 

.06126 

.22 

•  19885 

1.78 

.57661 

2-34 

•85015 

2.90 

.06471 

•23 

.2O70I 

1.79 

.58222 

2-35 

•85442 

2.91 

.06815 

.24 

.21511 

.80 

•58779 

2.36 

.85866 

2.92 

.07158 

•25 

.22314 

.81 

•59333 

2.37 

.86289 

2-93 

.07500 

.26 

.23111 

.82 

.59884 

2.38 

.86710 

2.94 

.07841 

.27 

.23902 

.83 

.  60432 

2.39 

.87129 

2.95 

.08181 

.28 

.  24686 

.84 

.60977 

2.40 

•87547 

2.96 

.08519 

.29 

•  25464 

.85 

.61519 

2.41 

.87963 

2-97 

.08856 

•30 

.26236 

.86 

.62058 

2.42 

.88377 

2.98 

.09192 

.31 

.27003 

.87 

•62594 

2.43 

.88789 

2-99 

.09527 

.32 

.27763 

.88 

•63127 

2.44 

.89200 

3.00 

.09861 

•33 

.28518 

.89 

•63658 

2.45 

.89609 

3.01 

.10194 

•34 

.29267 

.90 

.64185 

2.46 

.90016 

3-02 

.10526 

•35 

.30010 

.91 

.64710 

2.47 

.90422- 

3.03 

.10856 

1.36 

•30748 

.92 

•65233 

2.48 

.90826 

3.04 

.  i  i  i  86 

1.37 

.31481 

•93 

•65752 

2.49 

.91228 

3.05 

.11514 

1.38 

.32208 

.94 

.66269 

2.50 

.91629 

3.06 

.11841 

L39 

.32930 

.95 

.66783 

2.51 

.92028 

3.07 

.12168 

1.40 

•33647 

.96 

.67294 

2.52 

.92426 

3.08 

•12493 

1.41 

•34359 

•97 

.67803 

2.53 

.92822 

3.09 

.12817 

.42 

.35066 

.98 

.68310 

2.54 

•93216 

3.10 

.13140 

•43 

•35767 

•99 

.68813 

2.55 

.93609 

3.  II 

.13462 

•44 

•  36464 

2.00 

•69315 

2.56 

.94001 

3.12 

•13783 

•45 

•37156 

2.01 

.69813 

2-57 

•94391 

3.13 

.14103 

.46 

•37844 

2.02 

.70310 

2.58 

•94779 

3.14 

.14422 

•47 

•38526 

2.03 

.  70804 

2.59 

.95166 

3.15 

.14740 

.48 

.39204 

2.04 

•7I295 

2.60 

•95551 

3.16 

•15057 

.49 

.39878 

2.05 

.71784 

2.61 

•95935 

3.17 

•15373 

.50 

.40547 

2.06 

.72271 

2.62 

•96317 

3.18 

.15688 

•51 

.41211 

2.07 

•72755 

2.63 

.96698 

3.19 

.  16002 

.52 

.41871 

2.08 

•73237 

2.64 

.97078 

3.20 

•16315 

•53 

•42527 

2.09 

•737i6 

2.65 

•97454 

3.21 

.16627 

•54 

•43178 

2.10 

.74194 

2.66 

•97833 

3.22 

.16938 

•55 

•43825 

2.  II 

.  74669 

2.67 

.98208 

3.23 

1.17248 

.56 

.44460 

2.12 

.75142 

2.68 

.98^82 

3.24 

I.T7SS7 

162 


TABLE  I.  Continued.  —  HYPERBOLIC    LOGARITHMS. 


X' 

Loga- 

ja 

Loga- 

N. 

Loga- 

X. 

Loga- 

• 

rithm. 

HI  • 

rithm. 

rithm. 

rithm. 

! 

3-25 

17865 

3.81 

1.33763 

4-37 

1.47476  i 

4-93 

•59534 

3-26 

.18173 

3.82 

1-34025 

4.38 

I-47705 

4.94 

•59737 

3-27 

18479 

3-83 

1.34286 

4-39 

1-47933  ! 

4-95 

•  59939 

3-28 

18784 

3.84 

1-34547 

4.40 

1.48160  ] 

4.96 

.60141 

3-29 

19089  i 

3-85 

1.34807 

4.41 

1.48387  1 

4-97 

•60342 

3-30 

19392 

3.86 

1-35067 

4.42 

1.48614 

4.98 

•60543 

3-31 

3.87 

I-35325 

4-43 

1.48840  j 

4.99 

.60744 

3-32 

19996 

3-88 

I-35584 

4.44 

1.49065  | 

5.OO 

.60944 

3-33 

.  20297 

3.89 

1-35841 

4.45 

1.49290  j 

5.01 

.61144 

3-34 

•20597 

3.90 

1.36098 

4.46 

I-495I5 

5-02 

61343 

3.35 

.  20896 

I-36354 

4-47 

-49739 

5.03 

.61542 

3-36 

.21194 

3-92 

1.36609 

4.48 

i  .  49962 

5.04 

.61741 

3-37 

.21491 

3-93 

i  .  36864 

4.49 

1.50185 

5.05 

.61939 

3-38 

.21788 

3-94 

1.37118 

4.50 

i  .  50408 

5.06 

•62137 

3-39 

.22083 

3-95 

4.51 

i  .  50630 

5.07 

•62334 

3-40 

.22378 

3.96 

1.37624 

4.52 

1.50851 

5.08 

•62531 

.22671 

3.97 

I-37877 

4.53 

1.51072 

5.09 

.62728 

3-42 

.  22964 

3.98 

1.38128 

4-54 

i  51293 

.62924 

3-43 
3-44 

.23256 
•23547 

3-99 
4.00 

I.38379 
i  .'38629 

ts 

5.12 

.63120 
•63315 

3-45 

•23837 

4.01 

1.38879 

4.57 

-5I95I 

5.13 

•63511 

3-46 

.24127 

4.02 

1.39128 

4.58 

1.52170 

5.14 

63705 

3-47 

.24415 

4.03 

1-39377 

4-59 

1.52388 

5.15 

.63900 

3-48 

-24703 

4.04 

1.39624 

4.60 

1.52606 

5.16 

.64094 

3-49 

-  24990 

4.05 

1.39872 

4.61 

1.52823 

5.17 

.  64287 

3-50 

•25276 

4.06 

1.40118 

4.62 

L53039 

5.18 

.64481 

3-51 

4.07 

i  .  40364 

4.63 

1-53256 

5.19 

•  64673 

3-52 

.25846 

4.08 

1.40610 

4.64 

5.20 

.  64866 

3-53 

.26130 

4.09 

1.40854 

4-65 

i  "-53687 

5.21 

.  65058 

3-54 

.26412 

4.10 

1.41099 

4-66 

i  •  53902 

5.22 

•65250 

3-55 

-26695 

4.11 

1-41342 

4.67 

—  54n6 

5.23 

.65441 

3-56 

.26976 

4.12 

1-41585 

4-68 

-54330 

5.24 

.65632 

3-57 

•27257 

4.13 

1.41828 

4-69 

^-  54543 

5.25 

.65823 

3.58 

•2/536 

4.14 

i  .42070 

4.70 

i  54756 

5.26 

.66013 

3-59 

-27815 

4-15 

1.42311 

!  4-71 

i  54969  i 

5.27 

.  66203 

.28093 

4.16 

1-42552 

!  4.72 

1.55181  1 

5.28 

•  66393 

3*6i 

•28371 

4-17 

1.42792 

i  4-73 

1-55393  ! 

5.29 

.  66582 

3-62 

.28647 

4.18 

1-43031 

i  4-74 

-55604  | 

5.30 

.66771 

3.63 

.28923 

4.19 

1-43270 

4-75 

1.55814 

5.31 

.66959 

3.64 

.29198 

4.20 

4.76 

-56025 

5-32 

•67147 

•29473 
.29746 

4.21 
4.22 

I-43746 
1.43984 

4-77 
4.78 

1-56235  : 
1.56444 

5.33 
5.34 

•67335 
•67523 

3.67 

.30019 

4-23 

1.44220 

4-79 

1-56653  , 

5.35 

.67710 

3-68 

.30291 

4.24 

I-44456 

4.80 

1.56862 

5.36 

.67896 

3.69 

4-25 

i  .  44692 

4.81 

1.57070 

5.37 

.68083 

3-70 

•  30833 

4.26 

1.44927 

4.82 

^•57277 

5.38 

.68269 

4-27 

1.45161 

4.83 

1-57485 

5.39 

•68455 

3.72 

•31372 

4.28 

1-45395 

4.84 

1.57691 

5.40 

.  68640 

3-73 

.31641 

4.29 

1.45629 

4.85 

:  1-57898 

.68825 

3-74 

.31909 

4.30 

1.45861 

4.86 

!  1.58104 

5.42 

.69010 

3-75 

.32176 

4-31 

1.46094 

4-87 

1-58309 

5.43 

.69194 

3.76 

•32442 

4.32 

i  .46326 

4.88 

I  1-58515 

5.44 

.69378 

3.77 

•32707 

4-33 

I-46557 

4^89 

1.58719 

5-45 

.69562 

3.78 

.32972 

4-34 

1.46787 

1  4.90 

1.58924 

5.46 

•69745 

3-79 

•33237 

4.35 

i  .47018 

4.91 

1.59127 

5-47 

.69928 

3.8o 

4.36 

1.47247 

u  4.92 

I-5933I 

5.48 

1  .70111 

163 


TABLE  I.  Continued.  —  HYPERBOLIC    LOGARITHMS. 


X. 

Loga- 
rithm. 

N. 

Loga- 
rithm. 

1 
N. 

Loga- 
rithm. 

N. 

Loga- 
rithm. 

5-49 

1.70293 

6.05 

i  .  80006 

6.61 

1.88858 

7.17 

1.96991 

5-50 

1  -  70475 

6.06 

1.80171 

6.62 

1.89010 

7.18 

1.97130 

5-5i 

1.70656 

6.07 

1.80336 

6.63 

1.89160 

7.19 

1.97269 

5-52 

i  .  70838 

6.08 

1.80500 

6.64 

1.89311 

7.20 

1.97408 

5-53 

i  .71019 

6.09 

i  .  80665 

6.65 

1.89462 

7.21 

J-97547 

5-54 

1.71199 

6.10 

1.80829 

6.66 

1.89612 

7.22 

1.97685 

5-55 

1.71380 

6.  ii 

1.80993 

6.67 

1.89762 

7.23 

1.97824 

5-56 

1.71560 

6.12 

1.81156 

6.68 

1.89912 

7.24 

1.97962 

5-57 

1.71740 

6.13 

1.81319 

6.69 

1.90061 

7.25 

i  .98100 

5-58 

1.71919 

6.14 

1.81482 

6.70 

1.90211 

7.26 

1.98238 

5-59 

i  .  72098 

6.15 

1.81645 

6.71 

1.90360 

7.27 

1.98376 

5-6o 

1.72277 

6.16 

i.  81808 

6.72 

i  .90509 

7.28 

5.6i 

!•  72455 

6.17 

1.81970 

6.73 

1.90658 

7.29 

1.98650 

5.62 

1.72633 

6.18 

1.82132 

6.74 

i  .  90806 

7.30 

1.98787 

5.63 

I.728II 

6.19 

1.82294 

6.75 

1.90954 

7.31 

1.98924 

5.64 

I  .  72988 

6.20 

1.82455 

6.76 

i  .91102 

7.32 

1.99061 

5.65 

I.73I66 

6.21 

1.82616 

6.77 

1.91250 

7-33 

1.99198 

5.66 

!•  73342 

6.22 

1.82777 

6.78 

1.91398 

7-34 

J-  99334 

5.67 

!-  73519 

6.23 

1.82937 

6.79 

I-9I545 

7-35 

1.99470 

5.68 

I  •  73695 

6.24 

1.83098 

6.80 

i  .91692 

7.36 

i  .  99606 

5.69 

1.73871 

6.25 

1.83258 

6.81 

1.91839 

7-37 

1.99742 

5.70 

I  .  74047 

6.26 

1.83418 

6.82 

1.91986 

7-38 

1.99877 

5-71 

1.74222 

6.27 

I-83578 

6.83 

1.92132 

7-39 

2.00013 

5.72 

!•  74397 

6.28 

I-83737 

6.84 

1.92279 

7.40 

2.00148 

5-73 

J-74572 

6.29 

i  .  83896 

6.85 

1.92425 

7.41 

2.00283 

5-74 

1.74746 

6.30 

1.84055 

6.86 

1.92571 

7.42 

2.00418 

5-75 

i  .  74920 

6.31 

1.84214 

6.87 

1.92716 

7-43 

2.00553 

5-76 

i  .  75094 

6.32 

1.84372 

6.88 

1.92862 

7-44 

2.00687 

5-77 

1.75267 

6.33 

1.84530 

6.89 

1.93007 

7-45 

2.00821 

5.78 

i  .  75440 

6-34 

1.84688 

6.90 

I-93I52 

7.46 

2.00956 

1-75613 

6.35 

1.84845 

6.91 

1.93297 

7-47 

2.01089 

5.80 

1.75786 

6.36 

1-85003 

6.92 

1.93442 

7.48 

2.01223 

5.8i 

I-75958 

6.37 

1.85160 

6-93 

1.93586 

7-49 

2-01357 

5-82 

1.76130 

6.38 

I-853I7 

6.94 

1-93730 

7-50 

2.01490 

5-83 

i  .  76302 

6-39 

I-85473 

6.95 

1.93874 

2  .01624 

5|4 

1.76473 

6.40 

1.85630 

6.96 

1.94018 

7.52 

2.01757 

i  .  76644 

6.41 

1.85786 

6.97 

1.94162 

7.53 

2.01890 

5-86 

1.76815 

6.42 

1.85942 

6.98 

I-94305 

7-54 

2.02022 

5.87 

1.76985 

6.43 

1.86097 

6-99 

i  .  94448 

7-55 

2-02155 

5-88 

1.77156 

6.44 

1.86253 

7.00 

I-9459I 

7.56 

2.02287 

5.89 

1.77326 

6-45 

1.86408 

7.01 

1-94734 

7-57 

2.02419 

5.90 

!•  77495 

6.46 

1-86563 

7.02 

1.94876 

7.58 

2.02551 

1.77665 

6.47 

1.86718 

7.03 

1.95019 

7-59 

2  .02683 

5-92 

!•  77834 

6.48 

1.86872 

7.04 

1.95161 

7.60 

2.02815 

5-93 

i  .  78002 

6-49 

i  .87026 

7.05 

1-95303 

7.61 

2.02946 

5-94 

1.78171 

6.50 

1.87180 

7.06 

1-95444 

7.62 

2.03078 

5-95 

i  •  78339 

6.51 

1.87334 

7.07 

1.95586 

7.63 

2.03209 

5.96 

1.78507 

6.52 

1.87487 

7.08 

1.95727 

7.64 

2.03340 

5-97 

1.78675 

6.53 

1.87641 

7.09 

1.95869 

7.65 

2.03471 

5.98 

i  .  78842 

6.54 

1.87794 

7.10 

i  .  96009 

7.66 

2.03601 

5-99 

i  .  79009 

6.55 

1.87947 

7.11 

1.96150 

7.67 

2.03732 

6.00 

1.79176 

6.56 

i  .  88099 

7.12 

1.96291 

7.68 

2.03862 

6.01 

i  .  79342 

6.57 

1.88251 

7.13 

1.96431 

7.69 

2.03992 

6.02 

i  .  79509 

6.58 

1.88403 

7.14 

1.96571 

7.70 

2.04122 

6.03 

1.79675 

6.59 

1.88555 

7.15 

1.96711 

7.71 

2.04252 

6.04 

i  .  79840 

6.60 

1.88707 

7.16 

i  .96851 

7.72 

2.04381 

164 


TABLE  I.  Continued.—  HYPERBOLIC    LOGARITHMS. 


X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

X. 

Loga- 
rithm. 

7-73 

2.04511 

8.30 

2.11626  : 

8.87 

2.18267 

9.44 

2.24496 

7-74 

2  .  04640 

8.31 

2  .  1  1  746 

8.88 

2.  18380 

9.45 

2.24601 

7-75 

2.04769 

8.32 

2.II866 

8.89 

2.18493 

9.46 

2.24707 

7.76 

2.04898 

8.33 

2.II986 

8.90 

2.18605 

9.47 

2.24813 

7-77 

2.05027 

8.34 

2.  I2I06 

8.91 

2.18717 

9.48 

2  .  24918 

7-78 

2-05156 

8-35 

2.12226 

8.92 

2.18830 

9.49 

2.25024 

7-79 

2.05284 

8.36 

2.12346 

8-93 

2.18942 

9.50 

2.25129 

7.8o 

2.05412 

8-37 

2.12465 

8.94 

2.19054 

9.51 

2.25234 

7.81 

2.05540 

8.38 

2-12585 

8.95 

2.19165 

9.52 

2-25339 

7.82 

2.05668 

8-39 

2.12704 

8.96 

2.19277 

9.53 

2.25444 

7.83 

2-05796 

8.40 

2.12823 

8.97 

2.19389 

9.54 

2.25549 

7.84 

2.05924 

8.41 

2.  12942 

8.98 

2.19500 

9-55 

2-25654 

7.85 

2.06051 

8.42 

2.I306I 

8.99 

2.19611 

9.56 

2.25759 

7.86 

2.06179 

8.43 

2.I3I80 

9.00 

2.19722 

9-57 

2.25863 

7.87 

2  .  06306 

8.44 

2.13298 

9.01 

2.19834 

9.58 

2.25968 

7-88 

2-06433 

8-45 

2.I34I7 

9.02 

2.19944 

9-59 

2.26O72 

7.89 

2.06560 

8.46 

2-13535 

9.03 

2.20055 

9.60 

2.26176 

7.90 

2  .  06686 

8.47 

9.04 

2  .20166 

9.61 

2.26280 

7.91 

2.06813 

8.48 

2.I377I 

9.05 

2.  20276 

9.62 

2.26384 

7.92 

2  .  06939 

8-49 

2.13889 

9.06 

2.20387 

9.63 

2.26488 

7.93 

2.07065 

8.50 

2.14007 

9.07 

2.20497 

9.64 

2.26592 

7-94 

2.07191 

8.51 

2.  I4I24 

9.08 

2  .20607 

9.65 

2.26696 

7-95 

2.07317 

8.52 

2.14242 

9.09 

2.20717 

9.66 

2.26799 

7.96 

2-07443 

8.53 

2-14359 

9.10 

2.20827 

9.67 

2.26903 

7-97 

2.07568 

8.54 

2.14476 

9.11 

2.20937 

9.68 

2  .  27006 

7.98 

2.07694 

8.55 

2-14593 

9.12 

2.2IO47 

9.69 

2.27109 

7-99 

2.07819 

8.56 

2.14710 

9.13 

2.2II57 

9.70 

2.27213 

8.00 

2.07944 

8.57 

2.14827 

9.14 

2  .21266 

9.71 

2.27316 

8.01 

2.08069 

8.58 

2.14943 

9.15 

2-21375 

9.72 

2.27419 

8.02 

2.08194 

8.59 

2.  15060 

9.16 

2.21485 

9-73 

2.27521 

8.03 

2.08318 

8.60 

2.15176 

9.17 

2.21594 

9.74 

2.27624 

8.04 

2.08443 

8.61 

2.15292 

9.18 

2.21703 

9-75 

2.27727 

8.05 

2.08567 

8.62 

2.15409 

9.19 

2.  2l8l2 

9.76 

2.27829 

8.06 

2.08691 

8.63 

2.15524 

9.20 

2.  21920 

9-77 

2.27932 

8.07 

2.08815 

8.64 

2.  15640 

9.21 

2.22O29 

9.78 

2.28034 

8.08 

2-08939 

8.65 

2.15756 

9.22 

2.22138 

9-79 

2.28136 

8.09 

2  .  09063 

8.66 

2.15871 

9-23 

2.22246 

9.80 

2.28238 

8.10 

2.09186 

8.67 

2.15987 

9.24 

2.22351 

9.81 

2.28340 

8.  ii 

2.09310 

8.68 

2.  l6l02 

9.25 

2  .  22462 

9.82 

2.28442 

8.12 

2.09433 

8.69 

2.  16217 

9.26 

2.22570 

9-83 

2.28544 

8.13 

2-09556 

8.70 

2.16332 

9-27 

2.22678 

9.84 

2.28646 

8.14 

2.09679 

8.71 

2-16447 

9.28 

2.22786 

2.28747 

8.15 

2.09802 

8.72 

2.  16562 

9.29 

2.22894 

9.86 

2  .  28849 

8.16 

2.09924 

8.73 

2.  16677 

9.30 

2.23001 

9-87 

2.28950 

8.17 

2.10047 

8.74 

2.  16791 

9-31 

2.23109 

9.88 

2.29051 

8.18 

2.  10169 

8.75 

2.16905 

9-32 

2.23216 

9.89 

2.29152 

8.19 

2.I029I 

8.76 

2  .  I7O2O 

9-33 

2.23323 

9.90 

2-29253 

8.20 
8.21 

2.I04I3 
2-10535 

8-77 
8.78 

2.I7I34 

2.17248 

9-34 
9-35 

2.23431 
2.23538 

9.91 
9-92 

2.29354 
2-29455 

8.22 

2.10657 

8-79 

2.17361 

9.36 

2.23645 

9-93 

2.29556 

8.23 

2.10779 

8.80 

2.17475 

9-37 

2.23751 

9.94 

2.29657 

8.24 

2.10900 

8.81 

2.17589 

9.38 

2.23858 

9-95 

2.29757 

8.25 

2.  II02I 

8.82 

2.17702 

9-39 

2.23965 

9.96 

2.29858 

8.26 

2.  III42 

8.83 

2.17816 

9.40 

2.24071 

9-97 

2-29958 

8.27 

2.II263 

8.84 

2.17929 

9.41 

2.24177 

9.98 

2.30058 

8.28 

2.11384 

8.85 

2.18042 

9.42 

2.24284 

9.99 

2.30158 

8.29 

2.U505 

8.86 

2.l8l5S 

9-43 

2  .  24390 

INDEX 


ACCURACY  of  reducing  motions,  14. 
Accuracy  of  the  spring,  5. 
Action  of  the  steam  shown  by  the  diagram, 

41. 

Adjustment  of  the  cord,  34. 
Admission  line,  44. 
Allowance  for  piston  rod,  104. 
Angularity  of  cord  affecting  diagram,   147. 
Apparatus  for  testing  for  the  effect  of  long 

indicator  piping,  150,  152. 
Assembling  the   instrument,  36. 
Attachment  of  the  indicator,  28.. 

BACK  pressure  line,  67. 
Balancing  the  effort,  111. 
Brumbo  pulley,  13. 

Brumbo  pulley  affecting  diagram,  147. 
Buckeye  reducing  motion,  24. 

CARE  of  the  instrument,  1. 
Care  of  the  instrument  after  using,  39. 

Cause  of  drop  in  steam  line,  47-50. 

Centering  the  diagram,  34. 

Change    of    load    affecting    distribution    in 
compound  engine,  141. 

Clearance  affecting  compression,  72. 

Clearance;     effect    on    combined    diagrams 
from  compound  engines,   141. 

Clearance     line     located     from     expansion 
curve,  61. 

Clearance,  measurement  of,  155. 

Coffin  averaging  instrument,  94. 

Combining    diagrams    from    compound    en- 
gines, 135. 

Compound-engine  diagrams,  clearance  con- 
sidered, 139. 

Compound-engine   diagrams,  clearance  neg- 
lected, 134. 

Compression  affected  by  clearance,  72. 

Compression  and  clearance  loss,  74. 

Compression  in  condensing  engine,  71. 

Compression  line,  70. 

Computing    horse-power,    96. 

Connection  of  reducing  lever  to  cross-head, 
14,  15,  16. 


Connection  of  reducing  motion  to  the  in- 
strument, 32. 

Conventional  steam  chest  diagram,  49. 

Cord,  33. 

Cord  adjustment,  34. 

Corrected  diagrams  for  head  and  crank 
end,  112. 

Correcting  theoretical  M.E.P.  for  departures 
from  the  ideal,  118. 

Counterpressure  line,  67. 

Cushioning  effect  of  compression,  73. 

Cylinder  condensation,  50,  76. 

DEFECTS  of  pendulum  reducing  motion, 
14. 

Determination   of    leakage,    63. 

Determination  of  the  point  of  cut-off,  60. 

Diagram,  the  ideal,  41. 

Diagrams  for  head-  and  crank-end,  112. 

Diagrams  from  compound  engines,  clear- 
ance considered,  139. 

Diagrams  from  compound  engines,  clearance 
neglected,  134. 

Diagrams  taken  with  excessive  indicator 
piping,  153. 

Direction  of  lead  of  cord  for  pendulum 
reducing  motion,  13. 

Dirt  and  scale  in  indicator  piping,  31. 

Distortion  of  diagram  due  to  shortness  of 
pendulum  lever,  15. 

Distortion  of  diagram — varying  with  man- 
ner of  attachment  of  cord,  to  the  cross- 
head,  16,  17. 

Drawing  the  theoretical  expansion  curve,  55. 

Drop  in  compression  line,  75. 

Drop  in  steam  line,  47. 

Drum-spring  tension,  5. 

EARLY  release,  65. 
Economy  of  expansion,   53. 
Effect  of  brumbo  pulley  on  diagram  errors, 

147. 
Effect  of  change  of  load  in  compound  engine, 

144. 

Effect  of  clearance  on  compression,  72. 

167 


168 


INDEX 


Effect  of  clearance  on  M.E.P.,  114. 

Effect  of  compression  on  clearance  loss,  74. 

Effect  of  condensation  and  re-expansion,  61. 

Effect  of  long  indicator  piping,  on  diagram, 
149. 

Effect  of  quality  of  steam  on  expansion 
line,  61. 

Effect  of  receiver  capacity  on  the  com- 
bined diagram,  142. 

Effect  of  small  exhaust  pipe  on  back  pres- 
sure, 67. 

Effect  of  small  ports  on  back  pressure,  67. 

Effect  of  a  variable  cut-off  in  low-pressure 
cylinder,  142. 

Effect  on  diagram  of  angularity  of  cord,  147. 

Effect  on  diagram  of  length  of  reducing 
lever,  15. 

Errors  in  the  diagram,  145. 

Expansion,  ratio  of,  114. 

Experiments  with  excessive  piping,  149. 

Exhaust  line,  67. 

/"^  RAPHIC  method  of  determining  clear- 
\J     ance,  61,  161. 

HATCHET  planimeter,  92. 
Horse-power  constant,  100. 

Table  of,  107. 

Horse-power  corrected  for  piston  rod,  104. 
Horse-power  (definition),  96. 
Horse    power   developed    by    oaoli    separate 
stroke,  106. 

IMPROPER     connection     of     the    instru- 
ment, 29. 

Indicator  piping  affecting  diagram,  149. 
Indicator  piping  experiments,  149. 
Interchangeable    (right-    and    left-hand)    in- 
dicators, 31. 

LAW  of  expansion  of  steam,  55. 
Leads,  9. 
Leakage,  63. 

Length  of  diagram,  12,  89. 
Location  of  indicator  connection,  27. 
Loop  at  release,  65. 
Loop  in  compression  line,  75. 
Loss  of  pressure  between  boiler  and  steam 

chest,  47. 

Lost  motion  in  the  indicator,  3. 
Lubrication  of  the  instrument,   10. 


M 


.E.P.  affected  by  clearance,  114. 

Mean   effective   pressure    (definition), 
77. 

Mean    effective    pressure    by    computation, 
113. 


Mean  effective  pressure  from  diagram,  77. 
Mean   pressure   of  the   ideal   diagram,    115. 
Mean  pressure  per  pound  of  initial,  115. 

Table  of,  115. 
Measuring  clearance,  155. 
Measuring  loops,   82. 
Measuring  loops  with  planimeter,  88. 
Measuring  ordinates  on  the  diagram,  77. 
Measuring  scales,  9,  79. 

Methods    of    drawing    the    theoretical    ex- 
pansion curve,  55. 


N 


EGATIVE  loop,  82-88. 


PANTOGRAPH,  18. 
Pantograph  table,  19. 
Paper  suitable  for  cards,  10. 
Paper,  putting  on,  37. 
Parallelism,  3. 
Parallel  rules,  81. 
Pencil  holders,  6. 
Pendulum  lever,  11. 
Piping  affecting  diagram,  149. 
Piping  experiments,  149. 
Piston  rod  area  allowance,  104. 
Piston  speed,  97. 

Table  of,  101,  102. 
Planimeter,  83. 

Plotting  the  expansion  curve,  55. 
Point  of  "cut-off,  60. 
Point  of  release,  64. 
Proportional  movement  of  pencil,  4. 

RATIO  of  expansion,  114. 
Reading  the  planimeter,  85. 
Reading  the  vernier,  85. 

Receiver  capacity  affecting  distribution,  142. 
Reducing  motion,   11. 
Reducing  wheels,  26. 
Reduction  of  compound  engine  diagrams  to 

correct  scales  for  combining,  135. 
Relation  of  pressure  and  volume,  55. 
Release,  64. 
Removal    of    dirt    and    scale    in    indicator 

piping,  31. 

Right-  and  left-hand  instruments,  31. 
Rod  connection  for  reducing  lever,   16. 
Rule  for  horse-power,  96. 
Rule   for  mean  effective   pressure,    118. 
Rule  for  mean  pressure,  114. 
Rule   for  steam  accounted  for  by  indicator, 

123. 


s 


CALES,  9,  79. 

Selection  of  an  indicator,  1. 


INDEX 


169 


Separate  diagrams  for  head-  and  crank- 
end,  112. 

Setting  the  pantograph,  19. 

Slotted  connection  for  reducing  lever,  14,  15. 

Spacing  ordinates  on  the  diagram,  78. 

Springs,  5,  6,  7,  8,  36. 

Steam  accounted  for  by  the  indicator,  119. 

Steam-chest  diagrams,  49. 

Steam  consumption  from  the  diagram,  119. 

Steam  consumption  in  compound  engine, 
129. 

Steam  line,  47. 

Sweet's  method  for  measuring  clearance, 
160. 

TABLE   for   computing   mean   and  initial 
pressures,  points  of  cut-off  and  ratios 
of  expansion,  115. 
Table    for    computing    steam    consumption 

values  of  13750  W,  132. 
Table    for    computing    steam    consumption 

13750 
values  of  100  to  250  pounds,  131. 


Table    for    computing    steam    consumption 


values  of 


E  p   up  to  100  pounds,  125. 

Table  for  using  the  pantograph,  19. 

Table  of  horse-power  constants,  107. 

Table  of  hyperbolic  logarithms,  1G2. 

Table  of  ideal  mean  effective  pressures,  115. 

Tapping  the  cylinder,  27. 

Test  for  accuracy  of  reducing  motion,   26. 

Testing  the  spring,  5. 

VACUUM  springs,  7. 
Variable  cut-off  on  low-pressure   cyl- 
inder, 142. 
Variations  of  compression  with   back   pres- 

sure, 72. 
Vernier,  85. 

Volume  of  steam  per  hour  per  horse-power, 
table  of  125-131. 


W 


IRE,  used  as  indicator  cord,  33. 


•V^C*  THE 

UNIVERSE 

.CALiFQjrU 


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OCT  17  1834 


OCT     19 1936 


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YC  12889 


211748 


